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Graph with at most one cycle per component
In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. That is, it is a system of vertices and
Pseudoforest
Number of edges touching a vertex in a graph
is a directed pseudoforest if and only if every vertex has outdegree at most 1. A functional graph is a special case of a pseudoforest in which every
Degree_(graph_theory)
American mathematician (1914–2005)
Linear complementarity problem Max-flow min-cut theorem of networks Pseudoforest Vehicle routing problem Dantzig's simplex algorithm Dantzig–Wolfe decomposition
George_Dantzig
Topics referred to by the same term
also refer to: Bicycle (graph theory), a minimal graph that is not a pseudoforest An ace-to-five straight, a type of poker hand Bicycle crunch, an abdominal
Bicycle_(disambiguation)
definition of a property is also called an invariant of the graph. pseudoforest A pseudoforest is an undirected graph in which each connected component has
Glossary_of_graph_theory
Data structure hashing scheme
succeeds if and only if the cuckoo graph for this set of values is a pseudoforest, a graph with at most one cycle in each of its connected components.
Cuckoo_hashing
Index of articles associated with the same name
directed graph in which the cycle lengths have no nontrivial common divisor Pseudoforest, a directed or undirected graph in which every connected component includes
Cyclic_graph
Trail in which only the first and last vertices are equal
induced cycles or their complements of odd length greater than three Pseudoforest, a graph in which each connected component has at most one cycle Strangulated
Cycle_(graph_theory)
Self-self morphism
is not invertible. Finite endofunctions are equivalent to directed pseudoforests. For sets of size n there are nn endofunctions on the set. Particular
Endomorphism
Undirected, connected, and acyclic graph
they are known as Bethe lattices. Decision tree Hypertree Multitree Pseudoforest Tree structure (general) Tree (data structure) Unrooted binary tree Bender
Tree_(graph_theory)
Abstraction of unicyclic subgraphs
are the edges of G and whose independent sets are the edge sets of pseudoforests of G, that is, the edge sets in which each connected component contains
Bicircular_matroid
On coloring the edges of graphs
algorithm of Misra and Gries may be interpreted as constructing a directed pseudoforest P (a graph in which each vertex has at most one outgoing edge) on the
Vizing's_theorem
Number of spanning trees of a complete graph
between n-node trees with two distinguished nodes and maximal directed pseudoforests. A proof by double counting due to Jim Pitman counts in two different
Cayley's_formula
Proofs in enumerative combinatorics
n-node directed pseudoforests. If there are Tn n-node trees, then there are n2Tn trees with two designated nodes. And a pseudoforest may be determined
Combinatorial_proof
Maximal subgraph whose vertices can reach each other
very small. The largest component has logarithmic size. The graph is a pseudoforest. Most of its components are trees: the number of vertices in components
Component_(graph_theory)
Abstraction of linear independence of vectors
most one cycle ie a set of edges is independent if and only if it is a pseudoforest . In any directed or undirected graph G {\displaystyle G} let E {\displaystyle
Matroid
Measurement of graph sparsity
into k {\displaystyle k} pseudoforests, and conversely any partition of a graph's edges into k {\displaystyle k} pseudoforests leads to an outdegree- k
Degeneracy_(graph_theory)
Graph drawn with all edges intersecting
Based on Erdős' proof, one can infer that every linear thrackle is a pseudoforest, that is, a graph in which each connected component has at most one cycle
Thrackle
Graph with almost the max amount of edges
and graphs with arboricity k are exactly the (k,k)-sparse graphs. Pseudoforests are exactly the (1,0)-sparse graphs, and the Laman graphs arising in
Dense_graph
Subgraph with contracted edges
reduce the rank by one. In other contexts (such as with the study of pseudoforests) it makes more sense to allow the deletion of a cut-edge, and to allow
Graph_minor
Finiteness of sets of forbidden graph minors
characterizations: forests, linear forests (disjoint unions of path graphs), pseudoforests, and cactus graphs; planar graphs, outerplanar graphs, apex graphs (formed
Robertson–Seymour_theorem
Planar graph with 4 nodes and 5 edges
are forbidden minors, the family of graphs obtained is the family of pseudoforests. The full automorphism group of the diamond graph is a group of order
Diamond_graph
Number denoting a graph's closeness to a tree
families of graphs with bounded treewidth include the cactus graphs, pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian
Treewidth
One-by-one assignment of colors to graph vertices
find optimal colorings for certain classes of graphs, including trees, pseudoforests, and crown graphs. Markossian, Gasparian & Reed (1996) define a graph
Greedy_coloring
treewidth. Families of graphs with this property include the cactus graphs, pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian
Partial_k-tree
describe other important families of sparse graphs, including trees, pseudoforests, and graphs of bounded arboricity. Based on this characterization, it
Laman_graph
Number of forests a graph's edges may be partitioned into
slope number. The pseudoarboricity of a graph is the minimum number of pseudoforests into which its edges can be partitioned. Equivalently, it is the maximum
Arboricity
Invariant in graph theory
number 1, with a vertex ordering given by a breadth-first traversal. Pseudoforests and grid graphs also have queue number 1. Outerplanar graphs have queue
Queue_number
PSEUDOFOREST
PSEUDOFOREST
PSEUDOFOREST
PSEUDOFOREST
Male
Spanish
Spanish form of Latin Paulus, PABLO means "small."
Female
English
Variant spelling of English Susie, SUZIE means "lily."
Surname or Lastname
English (chiefly southern)
English (chiefly southern) : patronymic from the personal name Law (pet form of Lawrence).Perhaps a reduced form of Scottish or Irish McLeish. Compare McLaws.
Biblical
God the zealous; the zeal of God
Boy/Male
Indian, Kannada, Tamil
Good Character
Boy/Male
Hindu
One of the kauravas
Boy/Male
Arabic, Muslim
Glory of the Faith
Boy/Male
Gaelic Irish Scottish American
Form of Michael 'Who is like God?'.
Girl/Female
Bengali, Hindu, Indian, Kannada
Bhakti; Worship
Girl/Female
Muslim
Happiness
PSEUDOFOREST
PSEUDOFOREST
PSEUDOFOREST
PSEUDOFOREST
PSEUDOFOREST