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Problem in theoretical computer science
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G {\displaystyle G} and H {\displaystyle
Subgraph_isomorphism_problem
Unsolved problem in computational complexity theory
efficiently. This problem is a special case of the subgraph isomorphism problem, which asks whether a given graph G contains a subgraph that is isomorphic
Graph_isomorphism_problem
Graph made from a subset of another graph's nodes and their edges
the induced subgraph of all vertices adjacent to it. The induced subgraph isomorphism problem is a form of the subgraph isomorphism problem in which the
Induced_subgraph
NP-complete graph problem
graph theory, induced subgraph isomorphism is an NP-complete decision problem that involves finding a given graph as an induced subgraph of a larger graph
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
Bijection between the vertex set of two graphs
called an isomorphism class of graphs. The question of whether graph isomorphism can be determined in polynomial time is a major unsolved problem in computer
Graph_isomorphism
Index of articles associated with the same name
computer science, a maximum common subgraph may mean either: Maximum common induced subgraph, a graph that is an induced subgraph of two given graphs and has
Maximum_common_subgraph
path problem, directed and undirected. Induced subgraph isomorphism problem Graph intersection number Longest path problem Maximum bipartite subgraph or
List_of_NP-complete_problems
Complexity class
Knapsack problem Hamiltonian path problem Travelling salesman problem (decision version) Subgraph isomorphism problem Subset sum problem Clique problem Vertex
NP-completeness
Area of discrete mathematics
NP-complete problem. For example: Finding the largest complete subgraph is called the clique problem (NP-complete). One special case of subgraph isomorphism is
Graph_theory
conserved structures across multiple species. Subgraph isomorphism problem Induced subgraph isomorphism problem de Gastines, Etienne; Knippel, Arnaud (2024)
Maximum_common_edge_subgraph
Complexity class used to classify decision problems
(a polynomial number of times). The subgraph isomorphism problem of determining whether graph G contains a subgraph that is isomorphic to graph H. Turing
NP_(complexity)
with at least k vertices. This problem is NP-complete. It is a generalization of the induced subgraph isomorphism problem, which arises when k equals the
Maximum common induced subgraph
Maximum_common_induced_subgraph
Method for finding patterns in networks
it applies to the subgraph isomorphism problem (an NP-complete problem), where it yields polynomial time algorithms when the subgraph pattern that it is
Color-coding
Creating a new graph from an existing graph
occurrence of the pattern graph (pattern matching, thus solving the subgraph isomorphism problem) and by replacing the found occurrence by an instance of the
Graph_rewriting
In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph G {\displaystyle G} , find the maximal number of edges
Forbidden_subgraph_problem
whether a graph is uniquely determined by its vertex-deleted subgraphs. The snake-in-the-box problem: what is the longest possible induced path in an n {\displaystyle
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Graph coloring related to treedepth
number of subgraphs of treedepth at most q {\displaystyle q} , and can be used in algorithms for subgraph isomorphism and related problems. The number
Centered_coloring
Problem of finding similarity between graphs
the graph isomorphism problem. The problem of exact matching of a graph to a part of another graph is called subgraph isomorphism problem. Inexact graph
Graph_matching
Maximum number of colors in a greedy graph coloring
results on subgraph isomorphism in sparse graphs to search for atoms) for graphs of bounded expansion. However, on general graphs the problem is W[1]-hard
Grundy_number
Computational problem in graph theory
induced subgraph isomorphism problem. There is a similar problem of finding long induced cycles in hypercubes, called the coil-in-the-box problem. The snake-in-the-box
Snake-in-the-box
Logical formulation of graph properties
{\displaystyle u} . The subgraph isomorphism problem for a fixed subgraph H {\displaystyle H} asks whether H {\displaystyle H} appears as a subgraph of a larger graph
Logic_of_graphs
Task of computing complete subgraphs
clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph
Clique_problem
Conjecture in graph theory
Unsolved problem in mathematics Are graphs uniquely determined by their subgraphs? More unsolved problems in mathematics In graph theory, informally, the
Reconstruction_conjecture
Family of graphs whose shallow minors are sparse graphs
with these properties have efficient algorithms for problems including the subgraph isomorphism problem and model checking for the first order theory of
Bounded_expansion
Methodic assignment of colors to elements of a graph
removes them from the graph. These actions are repeated on the remaining subgraph until no vertices remain. The worst-case complexity of DSatur is O ( n
Graph_coloring
Graphs that differ only by edge subdivision
Determining whether for graphs G and H, H is homeomorphic to a subgraph of G, is an NP-complete problem. The reverse operation, smoothing out or smoothing a vertex
Homeomorphism_(graph_theory)
component algorithm Tarjan's strongly connected components algorithm Subgraph isomorphism problem Bitap algorithm: fuzzy algorithm that determines if strings are
List_of_algorithms
Graph representing edges of another graph
solve a problem in extremal graph theory, of constructing a graph with a given number of edges and vertices whose largest tree induced as a subgraph is as
Line_graph
Binary operation in graph theory
to isomorphisms of induced subgraphs of G and H. Therefore, the modular product graph can be used to reduce problems of induced subgraph isomorphism to
Modular_product_of_graphs
to isomorphism. It can be represented as an induced subgraph of G, and is a core in the sense that all of its self-homomorphisms are isomorphisms. 4. In
Glossary_of_graph_theory
Logical problem studied in computer science
theories (SMT) is the problem of determining whether a mathematical formula is satisfiable. It generalizes the Boolean satisfiability problem (SAT) to more complex
Satisfiability modulo theories
Satisfiability_modulo_theories
Graph layout on multiple half-planes
bounded expansion, the subgraph isomorphism problem, of finding whether a pattern graph of bounded size exists as a subgraph of a larger graph, can be
Book_embedding
Vertices whose removal breaks all cycles
graphs with bounded FVS number. Some examples are graph isomorphism and the path reconfiguration problem. unpublished results due to Garey and Johnson, cf.
Feedback_vertex_set
Type of computational problem
by k?". For all k≥2, ModkP contains the graph isomorphism problem. Further, the graph isomorphism problem is low in ModkP. When k is prime, the set of
Counting_problem_(complexity)
Graph made from disjoint union of complete graphs
overall graph is a homogeneous graph, meaning that every isomorphism between two of its induced subgraphs can be extended to an automorphism of the whole graph
Cluster_graph
Property of graphs that depends only on abstract structure
invariants are instrumental for fast recognition of graph isomorphism, or rather non-isomorphism, since for any invariant at all, two graphs with different
Graph_property
transaction) supports a given subgraph is an NP-complete problem, since it is an NP-complete instance of the subgraph isomorphism problem. Furthermore, due to
Frequent_subtree_mining
solution. This technique has given PTASs for the following problems: subgraph isomorphism, maximum independent set, minimum vertex cover, minimum dominating
Baker's_technique
Graph that can be embedded in the plane
in time O(v) whether they are isomorphic or not (see also graph isomorphism problem). Any planar graph on n nodes has at most 8(n-2) maximal cliques
Planar_graph
Statement in mathematical combinatorics
induced subgraphs. Roughly speaking, instead of finding a monochromatic subgraph, we are now required to find a monochromatic induced subgraph. In this
Ramsey's_theorem
Structure-preserving correspondence between node-link graphs
subgraph of H. If a homomorphism f : G → H is a bijection, and its inverse function f −1 is also a graph homomorphism, then f is a graph isomorphism.
Graph_homomorphism
Complexity class of problems
satisfiability problems cannot be in NPI. Some problems that are considered good candidates for being NP-intermediate are the graph isomorphism problem, and decision
NP-intermediate
Set of edges without common vertices
transport problem involves bipartite matching as a sub-problem. The subtree isomorphism problem involves bipartite matching as a sub-problem. Matching
Matching_(graph_theory)
Basic concept of graph theory
remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important
Connectivity_(graph_theory)
Israeli computer scientist and mathematician
technique for subgraph isomorphism. With Howard Karloff, he is the namesake of the Karloff–Zwick algorithm for approximating the MAX-3SAT problem of Boolean
Uri_Zwick
Graph of chess rook moves
graphs are connected-homogeneous, meaning that every isomorphism between two connected induced subgraphs can be extended to an automorphism of the whole graph
Rook's_graph
Cubic graph with 10 vertices and 15 edges
Eulerian subgraph of a graph G is a subgraph consisting of a subset of the edges of G, touching every vertex of G an even number of times. These subgraphs are
Petersen_graph
Estimate of time taken for running an algorithm
Subgroup Problem with Polynomial Space". arXiv:quant-ph/0406151v1. Grohe, Martin; Neuen, Daniel (2021). "Recent advances on the graph isomorphism problem". In
Time_complexity
16-regular graph with 27 vertices and 216 edges
graph is defined to be k-ultrahomogeneous if every isomorphism between two of its induced subgraphs of at most k vertices can be extended to an automorphism
Schläfli_graph
Infinite graph containing all countable graphs
isomorphic finite subgraphs of the Rado graph extends their isomorphism to an automorphism of the entire Rado graph. The fact that every isomorphism of finite
Rado_graph
Graph formed by complementation and disjoint union
constructing their cotrees and applying a linear time isomorphism test for labeled trees. If H is an induced subgraph of a cograph G, then H is itself a cograph;
Cograph
Computational complexity class
n)}} . Problems for which a quasi-polynomial time algorithm has been announced but not fully published include: The graph isomorphism problem, determining
Quasi-polynomial_time
One of two different regular graphs with 16 vertices
is also connected-homogeneous, meaning that every isomorphism between two connected induced subgraphs can be extended to an automorphism of the whole graph
Clebsch_graph
Unsolved problem on graph query complexity
for testing whether the graph has a subgraph isomorphic to any given graph (the so-called subgraph isomorphism problem), the best known lower bound is Ω
Aanderaa–Karp–Rosenberg conjecture
Aanderaa–Karp–Rosenberg_conjecture
Subunit of a computational problem
provided gadgets for reducing the problem of finding a subgraph with given degree constraints to a perfect matching problem. However, the "gadget" terminology
Gadget_(computer_science)
1979 classic textbook on computational complexity theory
original names) are: Graph isomorphism This problem is known to be in NP, but it is unknown if it is NP-complete. Subgraph homeomorphism (for a fixed
Computers_and_Intractability
Generalization of graph theory
can have any cardinality, there are several notions of the concept of a subgraph, called subhypergraphs, partial hypergraphs and section hypergraphs. Let
Hypergraph
Subgraph with contracted edges
removal splits G into two (possibly disconnected) subgraphs with at most 2n⁄3 vertices per subgraph. Even stronger, for any fixed H, H-minor-free graphs
Graph_minor
Type of dominating set in graph theory
function f = ( V 0 , V 1 , V 2 ) {\displaystyle f=(V_{0},V_{1},V_{2})} : The subgraph induced by V 1 {\displaystyle V_{1}} has maximum degree at most 1. No edge
Roman_dominating_set
Undirected, connected, and acyclic graph
unlabeled free trees is a harder problem. No closed formula for the number t(n) of trees with n vertices up to graph isomorphism is known. The first few values
Tree_(graph_theory)
Graph of numbers differing by a square
quasi-random: the number of times each possible constant-order graph occurs as a subgraph of a Paley graph is (in the limit for large q) the same as for random graphs
Paley_graph
Soviet Ukrainian mathematician (1937–2017)
definition of the modular product of graphs as a way of reducing subgraph isomorphism problems to finding maximum cliques in graphs.[V74] He also proved a
Vadim_G._Vizing
Award for advancements in discrete mathematics
characterization of the weakly bipartite graphs (graphs whose bipartite subgraph polytope is 0-1). Satoru Iwata, Lisa Fleischer, Satoru Fujishige, and Alexander
Fulkerson_Prize
Type of sub-graph
u, v ∈ V′. The mapping f is called an isomorphism between G and G′. When G″ ⊂ G and there exists an isomorphism between the sub-graph G″ and a graph G′
Network_motif
Mapping of mathematical formulas to a particular meaning
notion of induced substructure is more restrictive than the notion of subgraph. For example, let G {\displaystyle G} be a graph consisting of two vertices
Structure (mathematical logic)
Structure_(mathematical_logic)
Number of edges touching a vertex in a graph
to isomorphism by its degree sequence is called unigraph and the corresponding degree sequence is called unigraphic. The degree sequence problem is the
Degree_(graph_theory)
Method of finding chemicals in a database
1351/goldbook.MT07069. Ullmann, J. R. (1976). "An Algorithm for Subgraph Isomorphism". Journal of the ACM. 23: 31–42. doi:10.1145/321921.321925. McMurry
Substructure_search
Class of artificial neural networks
memory requirements by operating on subgraphs rather than the full graph. Cluster-GCN partitions the graph into subgraphs using graph partitioning algorithms
Graph_neural_network
On linear-time algorithms for graph logic
u and v. The vertices in a bag can be thought of as the terminals of a subgraph of G, represented by the subtree of the tree decomposition descending from
Courcelle's_theorem
Chordal graph where all cycles of even length have odd chords
can be solved efficiently for strongly chordal graphs. Graph isomorphism is isomorphism-complete for strongly chordal graphs. Hamiltonian Circuit remains
Strongly_chordal_graph
Mathematical set of all subsets of a set
be applied to the example above, in which S = {x, y, z}, to get the isomorphism with the binary representations of numbers from 0 to 2n − 1, with n being
Power_set
Algebraic encoding of graph connectivity
{\displaystyle k(A)} is the number of connected components of the spanning subgraph (V,A). This is related to the corank-nullity polynomial by Q G ( u , v
Tutte_polynomial
Structure in mathematical logic
induced from the bigger structure. Subgraphs are an example where the distinction matters, and the term "subgraph" does indeed refer to weak substructures
Substructure_(mathematics)
American mathematician
Retrieved 2019-11-29. Rossman, Benjamin (2019). "Lower Bounds for Subgraph Isomorphism". In Boyan, Sirakov; De Souza, Paulo Ney; Viana, Marcelo (eds.).
Benjamin_Rossman
popular classification criteria is graph isomorphism, not to be confused with crystallographic isomorphism. Two periodic graphs are often called topologically
Periodic_graph_(geometry)
Two closely related models for generating random graphs
Łuczak) is known when P is monotone with respect to the subgraph ordering (meaning that if A is a subgraph of B and B satisfies P, then A will satisfy P as well)
Erdős–Rényi_model
Axiom of set theory
connected graph can be extended to a spanning tree, while every spanning subgraph contains a spanning tree. Several results in category theory invoke the
Axiom_of_choice
Function in algebraic graph theory
where t ( G ) {\displaystyle t(G)} is the number of triangles (3-cycle subgraphs) in G {\displaystyle G} . The coefficient of x 1 {\displaystyle x^{1}}
Chromatic_polynomial
Solid with twenty equal triangular faces
its edges, and the removal of any two of its vertices leaves a connected subgraph. According to Steinitz's theorem, the icosahedral graph endowed with these
Regular_icosahedron
Argentine-born American mathematician
monochromatic 4-cycle or 6-cycle). (b) Which vertex-transitive induced subgraphs does a hypercube have? The Dejter graph mentioned above is 6-regular,
Italo_Jose_Dejter
Invariant in graph theory
depth of the minor. As a consequence, several algorithmic problems including subgraph isomorphism for pattern graphs of bounded size have linear time algorithms
Queue_number
Homotopic map of a graph
(which, in this case, means that τ is a continuous map which induces an isomorphism at the level of fundamental groups). f : Γ → Γ is a combinatorial map
Train_track_map
analysis. Problems of this type include subgraph isomorphism for subgraphs of bounded size, and the vertex cover and dominating set problems for covers
Twin-width
Model of computational complexity
Query Complexities", arXiv:quant-ph/0501142 Huang, Hao (2019). "Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture". Annals of Mathematics
Decision_tree_model
Characterizes the height of any finite partially ordered set
of perfect graphs. An undirected graph is perfect if, in every induced subgraph, the chromatic number equals the size of the largest clique. In the comparability
Mirsky's_theorem
Data structure for Boolean functions
following two rules have been applied to its graph: Merge any isomorphic subgraphs. Eliminate any node whose two children are isomorphic. In popular usage
Binary_decision_diagram
Graph formed by subdivision of triangles
degree-one vertices, and compression of degree-two vertices. In every subgraph of an Apollonian network, the most recently added vertex has degree at
Apollonian_network
Romanian-american computational chemist
the automatic indexing of organic reactions using Maximum common subgraph isomorphism algorithms, which became foundational for many reaction database
George_Vladutz
Model for mathematical theories
saturated, because any complete type is isolated (implied) by the finite subgraph consisting of the variables and parameters used to define the type. Both
Saturated_model
Operation in graph theory
defined by replacing the subgraph of G {\displaystyle G} induced by N G ( v ) {\displaystyle N_{G}(v)} with its complementary subgraph. In other words, two
Local_complementation
Graph linking pairs of comparable elements in a partial order
Comparability graphs can also be characterized by a list of forbidden induced subgraphs. A cocomparability graph is the complement of a comparability graph. That
Comparability_graph
Branch of mathematical logic
Bruijn–Erdős theorem for countable graphs: every countable graph whose finite subgraphs are k-colorable is k-colorable. The system ACA0 adds to RCA0 the comprehension
Reverse_mathematics
comparability graph that form the disjoint union of two subgraphs or that connect two subgraphs by all possible edges; these two operations are the basic
Series-parallel_partial_order
Test of a specified bit in a binary number
contains every finite undirected graph as an induced subgraph, and any isomorphism of its induced subgraphs can be extended to a symmetry of the whole graph
BIT_predicate
Graph-theoretic description of polyhedra
{\displaystyle G} leaves the rest of G {\displaystyle G} as a connected subgraph. Such cycles are called peripheral cycles. Thus, the combinatorial structure
Steinitz's_theorem
Algebraic surface defined by a cubic polynomial
whenever two lines meet. This graph was analyzed in the 19th century using subgraphs such as the Schläfli double six configuration. The complementary graph
Cubic_surface
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