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Non-crossing graph with vertices on outer face
graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar graphs
Outerplanar_graph
Type of planar graph
In graph theory, a k-outerplanar graph is a planar graph that has a planar embedding in which the vertices belong to at most k {\displaystyle k} concentric
K-outerplanar_graph
Graph that can be embedded in the plane
results in a (k − 1)-outerplanar embedding. A graph is k-outerplanar if it has a k-outerplanar embedding. A Halin graph is a graph formed from an undirected
Planar_graph
Graph containing cycles of all possible lengths
maximal outerplanar graph is a graph formed by a simple polygon in the plane by triangulating its interior. Every maximal outerplanar graph is pancyclic
Pancyclic_graph
Oriented graph, used by some authors as a synonym for a directed graph. out-degree See degree. outer See face. outerplanar An outerplanar graph is a graph that
Glossary_of_graph_theory
Graph layout on multiple half-planes
complete graphs. The graphs with book thickness one are the outerplanar graphs. The graphs with book thickness at most two are the subhamiltonian graphs, which
Book_embedding
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
as a minor; an outerplanar graph cannot contain K3,2 as a minor (These are not sufficient conditions for planarity and outerplanarity, but necessary)
Complete_bipartite_graph
Sharpest angle between edges at a vertex
Nonetheless, every outerplanar graph of maximum degree d has an outerplanar drawing with angular resolution proportional to 1/d. For planar graphs with maximum
Angular resolution (graph drawing)
Angular_resolution_(graph_drawing)
Subgraph induced by all nodes linked to a given node of a graph
any Turán graph is locally Turán. Every planar graph is locally outerplanar. However, not every locally outerplanar graph is planar. A graph is triangle-free
Neighbourhood_(graph_theory)
Petersen graph Planar graph Dual polyhedron Outerplanar graph Random graph Regular graph Scale-free network Snark (graph theory) Sparse graph Sparse graph code
List_of_graph_theory_topics
Measurement of graph sparsity
5-degenerate, and the degeneracy of any planar graph is at most five. Similarly, every outerplanar graph has degeneracy at most two, and the Apollonian
Degeneracy_(graph_theory)
Conjecture in graph theory
complete graph. Trees Disconnected graphs Unit interval graphs Separable graphs without end vertices Maximal planar graphs Maximal outerplanar graphs Outerplanar
Reconstruction_conjecture
Partition of a simple polygon into triangles
cases of planar straight-line graphs. When there are no holes or added points, triangulations form maximal outerplanar graphs. Over time, a number of algorithms
Polygon_triangulation
Special labeling in graph theory
for certain cubic graphs such as cubic Hamiltonian graphs. He showed that in case of outerplanar graph of maximum degree 4, the incidence chromatic number
Incidence_coloring
polynomial time using maximum weight matching in bipartite graphs. For outerplanar graphs of bounded degree, a polynomial-time dynamic programming algorithm
Maximum_common_edge_subgraph
Intersection graph of a chord diagram
graph. Every outerplanar graph is also a circle graph. The circle graphs are generalized by the polygon-circle graphs, intersection graphs of polygons
Circle_graph
Graph property
complement of an n-vertex graph is a linear forest, then μ ≥ n − 3; If the complement of an n-vertex graph is outerplanar, then μ ≥ n − 4; If the complement
Colin de Verdière graph invariant
Colin_de_Verdière_graph_invariant
Graph where all long cycles have a chord
planar graphs, or equivalently planar 3-trees. Maximal outerplanar graphs are a subclass of 2-trees, and therefore are also chordal. Chordal graphs are a
Chordal_graph
Graph representing faces of another graph
plane graph is the subgraph of the dual graph whose vertices correspond to the bounded faces of the primal graph. A plane graph is outerplanar if and
Dual_graph
Mathematical tree of cycles
cut-vertex) is an edge or a cycle. Cacti are outerplanar graphs. Every pseudotree is a cactus. A nontrivial graph is a cactus if and only if every block is
Cactus_graph
Describing a family of graphs by excluding certain (sub)graphs
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to
Forbidden graph characterization
Forbidden_graph_characterization
Number of vertices with unambiguous distances
for outerplanar graphs. The same authors proved that n ≤ ( D β + 1 ) t − 1 {\displaystyle n\leq (D\beta +1)^{t-1}} for graphs with no complete graph of
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
Graph with almost the max amount of edges
graphs are (3,6)-sparse. However, not every (3,6)-sparse graph is planar. Similarly, outerplanar graphs are (2,3)-sparse and planar bipartite graphs are
Dense_graph
Coloring in which edges are labeled by integers
is a connected bipartite graph and G ∈ N, then W(G) ≤ diam(G) (∆(G) − 1) + 1. Interval edge-colorings of outerplanar graphs were investigated by Giaro
Interval_edge_coloring
Finiteness of sets of forbidden graph minors
path graphs), pseudoforests, and cactus graphs; planar graphs, outerplanar graphs, apex graphs (formed by adding a single vertex to a planar graph), toroidal
Robertson–Seymour_theorem
Representation of a graph as a path graph "thickened" by some amount
polynomial time for graphs of bounded treewidth including series–parallel graphs, outerplanar graphs, and Halin graphs, as well as for split graphs, for the complements
Pathwidth
Graph theory model
series–parallel graphs, and include also the maximal outerplanar graphs. Planar 3-trees are also known as Apollonian networks. The graphs that have treewidth
K-tree
Graph coloring with an allowed number of same-color neighbors
subgraph of an outerplanar graph is outerplanar and every graph obtained by contracting edges of an outerplanar graph is outerplanar. This implies that
Defective_coloring
(1, 5)-decomposable if G {\displaystyle G} has no 4-cycles. Every outerplanar graph is F(2, 0)-decomposable and (1, 3)-decomposable. Gonçalves (2009)
(a,_b)-decomposition
Class of mathematical games
_{g}({\mathcal {C}})=5} . Outerplanar graphs: 6 ≤ χ g ( O ) ≤ 7 {\displaystyle 6\leq \chi _{g}({\mathcal {O}})\leq 7} . Planar graphs: 7 ≤ χ g ( P ) ≤ 17 {\displaystyle
Graph_coloring_game
Families of graphs with this property include the cactus graphs, pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian
Partial_k-tree
Size of bounding box of graph drawing
near-linear area, depending on the drawing style. Every outerplanar graph has a straight-line outerplanar drawing with area subquadratic in its number of vertices
Area_(graph_drawing)
Recursively-formed graph with two terminal vertices
problems. The class of GSP-graphs include the classes of SP-graphs and outerplanar graphs. GSP graphs may be specified by Definition 2 augmented with the third
Series–parallel_graph
Graph which can be made planar by removing a single node
For instance, adding a single vertex to an outerplanar graph (a graph with τ = 1) produces a planar graph. When G \ {v} is 3-connected, this bound is
Apex_graph
Graph with tight clique-coloring relation
forests, the interval graphs, and the maximal outerplanar graphs. The split graphs are exactly the graphs that are chordal and have a chordal complement
Perfect_graph
On graph drawing with integer edge lengths
the empty graph by the removal only of vertices of degree at most two (the 2-degenerate planar graphs) include both the outerplanar graphs and the series–parallel
Harborth's_conjecture
{\displaystyle k} -outerplanar graph. Many NP-complete problems can be solved with dynamic programming on k {\displaystyle k} -outerplanar graphs. Baker's technique
Baker's_technique
Graph with edges non-crossing and upward
upward planar drawing for these graphs may be tested in polynomial time. Testing whether an outerplanar directed acyclic graph has an upward planar drawing
Upward_planar_drawing
time for outerplanar graphs. There is a constant-factor approximation algorithm for interval graphs and for bipartite graphs. The interval graph case remains
Sum_coloring
Graph with at most one crossing per edge
1-planar graph. The class of graphs analogous to outerplanar graphs for 1-planarity are called the outer-1-planar graphs. These are graphs that can be
1-planar_graph
Adding edges to make a graph Hamiltonian
certain classes of graphs, including series–parallel graphs and their subgraphs, which include outerplanar graphs, as well as for a line graph of a tree or
Hamiltonian_completion
possible to find such an embedding when both of the two given graphs are outerplanar graphs and their intersection is a linear forest, with at most one
Simultaneous_embedding
Points usable to draw any planar graph
remains universal for outerplanar graphs. Planar graphs that can be partitioned into nested cycles, 2-outerplanar graphs and planar graphs of bounded pathwidth
Universal_point_set
NP-complete graph problem
separates outerplanar graphs from their generalization series–parallel graphs: it may be solved in polynomial time for 2-connected outerplanar graphs, but
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
Number denoting a graph's closeness to a tree
the cactus graphs, pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian networks. The control-flow graphs arising in
Treewidth
On linear-time algorithms for graph logic
for graphs of treewidth at most three, for k-connected graphs of treewidth k, for graphs of constant treewidth and chordality, and for k-outerplanar graphs
Courcelle's_theorem
Any planar graph can be subdivided by removing a few vertices
N.; Sýkora, O.; Vrt'o, I. (1993), "Edge separators of planar and outerplanar graphs with applications", Journal of Algorithms, 14 (2): 258–279, doi:10
Planar_separator_theorem
bounded pathwidth, the 2-clique-sums of graphs of bounded size, and the k {\displaystyle k} -outerplanar graphs. In contrast to the behavior of metric
GNRS_conjecture
Embedding a graph in 3D space with no cycles interlinked
well-known: the graphs with μ ≤ 1 are the linear forests (disjoint unions of paths), the graphs with μ ≤ 2 are the outerplanar graphs, and the graphs with μ ≤
Linkless_embedding
Mathematical tree with cycle through leaves
Shan-Chen (2002), "The incidence coloring number of Halin graphs and outerplanar graphs", Discrete Mathematics, 256 (1–2): 397–405, doi:10.1016/S0012-365X(01)00302-8
Halin_graph
Graph drawing with vertices on a circle
zero only for outerplanar graphs. For other graphs, it may be optimized or reduced separately for each biconnected component of the graph before combining
Circular_layout
Invariant in graph theory
traversal. Pseudoforests and grid graphs also have queue number 1. Outerplanar graphs have queue number at most 2; the 3-sun graph (a triangle with each of its
Queue_number
Function in algebraic graph theory
class includes cographs and graphs of bounded tree-width, such as outerplanar graphs. The deletion-contraction recurrence gives a way of computing the
Chromatic_polynomial
Subgraph of planar graph with Hamiltonian cycle
graph is always subhamiltonian. Heath, Lenwood S. (1987), "Embedding outerplanar graphs in small books", SIAM Journal on Algebraic and Discrete Methods, 8
Subhamiltonian_graph
Numerical invariant of graphs
log n ) {\displaystyle O(t\log n)} . Since outerplanar graphs, series–parallel graphs, and Halin graphs all have bounded treewidth, they all also have
Tree-depth
Graph coloring with equal color classes
to Chen & Lih 1994) and outerplanar graphs. A polynomial time algorithm is also known for equitable coloring of split graphs. However, Fellows et al.
Equitable_coloring
(2013-12-01). "A polynomial-time maximum common subgraph algorithm for outerplanar graphs and its application to chemoinformatics". Annals of Mathematics and
Maximum common induced subgraph
Maximum_common_induced_subgraph
Smallest dimension where a graph can be represented as an intersection graph of boxes
graphs is G. Every outerplanar graph has boxicity at most two, and every planar graph has boxicity at most three. If a bipartite graph has boxicity two
Boxicity
Tree graph with all nodes within distance 1 from central path
time algorithms if a graph is an outerplanar, a series-parallel, or a Halin graph. Caterpillar trees have been used in chemical graph theory to represent
Caterpillar_tree
Unsolved problem on graph coloring
"Thickness-two graphs, II: More new nine-critical graphs, independence ratio, cloned planar graphs, and singly and doubly outerplanar graphs", Graphs and Combinatorics
Earth–Moon_problem
Cycles in a graph that generate all cycles
basis, and is fundamental if and only if the embedding of the graph is outerplanar. For graphs properly embedded onto other surfaces so that all faces of
Cycle_basis
Graph formed from disjoint paths
Deepak (February 10–12, 2022), "B0-VPG Representation of AT-free Outerplanar Graphs", written at Puducherry, India, in Balachandran, Niranjan; Inkulu
Linear_forest
American mathematician and computer scientist
Hedetniemi. Her dissertation was Algorithms on Trees and Maximal Outerplanar Graphs: Design, Complexity Analysis, and Data Structures Study. She joined
Sandra_Mitchell_Hedetniemi
(which generate each other, and no other simple graphs) are the excluded minors for outerplanar graphs and μ ≤ 2 {\displaystyle \mu \leq 2} . K 5 {\displaystyle
Heawood_family
Topological Graph Theory, Courier Dover Publications, 151 Gross, Jonathan L. (2011), "Genus Distributions of Cubic Outerplanar Graphs", Journal of Graph Algorithms
Graph_amalgamation
Type of total coloring in graph theory
Weifan (2010). "Adjacent vertex distinguishing total colorings of outerplanar graphs". Journal of Combinatorial Optimization. 19 (2): 123–133. doi:10
Adjacent-vertex-distinguishing-total coloring
Adjacent-vertex-distinguishing-total_coloring
OUTERPLANAR GRAPH
OUTERPLANAR GRAPH
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Surname or Lastname
German (also Gräff), Dutch, and Jewish (Ashkenazic)
German (also Gräff), Dutch, and Jewish (Ashkenazic) : variant of Graf.English : metonymic occupational name for a clerk or scribe, from Anglo-Norman French grafe ‘quill’, ‘pen’ (a derivative of grafer ‘to write’, Late Latin grafare, from Greek graphein).
Boy/Male
Spanish American Italian Latin
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
OUTERPLANAR GRAPH
OUTERPLANAR GRAPH
Male
Hebrew
(×’Ö¼ï‹×’) Hebrew name GOWG means "mountain." In the bible, this is the name of a son of Shemaiah and the name of the prophetic prince of the land of Magog.Â
Boy/Male
Arabic, Muslim, Sindhi
Sullen
Girl/Female
American, British, English, Latin
Modern Variant of Candace; Ancient Hereditary Title Used by Ethiopian Queens; Fire White; Glowing White
Girl/Female
American, Australian
Fairy Princess of the Field
Girl/Female
Greek American English
Well born.
Boy/Male
Indian
Owner
Girl/Female
Hebrew
Devoted to God.
Girl/Female
Afghan, Arabic, Danish, Indian, Muslim, Parsi, Sanskrit
Friend
Boy/Male
Arabic, Muslim
Servant of the Most Merciful
Boy/Male
Irish
Brave.
OUTERPLANAR GRAPH
OUTERPLANAR GRAPH
OUTERPLANAR GRAPH
OUTERPLANAR GRAPH
OUTERPLANAR GRAPH
a.
Resembling graphite or plumbago.
a.
Alt. of Graphical
a.
Alt. of Graphitoidal
n.
A pen-shaped pointing device used to specify the cursor position on a graphics tablet.
n.
Hence, any graphic or vivid delineation or description of a person; as, a portrait in words.
n.
An instrument which, when applied over an artery, indicates graphically the movements or character of the pulse. See Sphygmogram.
n.
An instrument for recording graphically the variations of temperature, or the indications of a thermometer.
n.
An instrument for measuring, and recording graphically, the pressure of the blood in any of the blood vessels of a living animal; -- called also kymographion.
n.
Same as Graphite.
a.
Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulae. See under Formula.
n.
Anything which represents graphically a succession of events, states, or acts; as, an historical map.
n.
A crucible; as, a graphite pot; a melting pot.
n.
See Graphoscope.
adv.
In a graphic manner; vividly.
a.
Having the faculty of, or characterized by, clear and impressive description; vivid; as, a graphic writer.
a.
Pertaining to, containing, derived from, or resembling, graphite.
n.
A mineral, a telluride of gold and silver, of a steel-gray, silver-white, or brass-yellow color. It often occurs in implanted crystals resembling written characters, and hence is called graphic tellurium.
n.
A chart or graphic representation of the average distribution of rain over the surface of the earth.
n.
The quality or state of being graphic.
n.
Alt. of Graphicalness