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{{Short description|Undirected graph with graph distances linearly bounded w.r.t. Euclidean distances}} [[File:Yao graph.svg|thumb|right|200px]] ...

...finding a graph <math>H</math> with as many edges as possible which is [[graph isomorphism|isomorphic]] to both a [[Glossary_of_graph_theory#Subgraphs|sub ...omorphism]]: a graph <math>H</math> is isomorphic to a subgraph of another graph <math>G</math> if and only if the maximum common edge subgraph of <math>G</ ...

...crete mathematics)|graph]] [[reachability]] and [[Computational complexity theory#Complexity classes|complexity classes]].{{fact|date=May 2016}} ...there is an edge from one configuration to another if it corresponds to a computational step of the model.{{fact|date=May 2016}} ...

...The problem asks whether a given list of pairs can be used to construct a graph, and for the list above, the answer is yes.]] ...v_i</math> has [[directed graph|indegree]] <math>a_i</math> and [[directed graph|outdegree]] <math>b_i</math>. ...

...[[Minimum spanning tree|minimal spanning subtrees]] containing the leaves in <math>L'</math>, of <math>T_1\mid S,\ldots, T_m\mid S</math> are the "same ....|last2=Keselman|first2=D.|date=1997-12-01|title=Maximum Agreement Subtree in a Set of Evolutionary Trees: Metrics and Efficient Algorithms|journal=SIAM ...

{{Short description|Existence of a graph with a degree sequence}} ...such that <math>(d_1,\dots,d_n)</math> is the [[degree sequence]] of this graph. ...

{{Short description|Unsolved problem in parallel algorithms}} ...ph connectivity]]. The input to the problem is a [[regular graph|2-regular graph]], forming either a single connected <math>n</math>-vertex cycle or two dis ...

[[File:Rhombic dodecahedron linear arboricity.svg|thumb|Partition of the graph of a [[rhombic dodecahedron]] into two [[linear forest]]s, showing that its ...city is a variant of [[arboricity]], the minimum number of [[forest (graph theory)|forest]]s into which the edges can be partitioned. ...

{{Short description|Finding the largest graph of given diameter and degree}} ...cs|Given two positive integers {{mvar|d}}, {{mvar|k}}, what is the largest graph of diameter {{mvar|k}} such that all vertices have degrees at most {{mvar|d ...

...oughgarden, T., Seshadhri, C., Wei, F., & Wein, N. (2020). Finding Cliques in Social Networks: A New Distribution-Free Model. ''SIAM Journal on Computing ...k]]s. For that reason, limiting the number of possible maximal cliques has computational ramifications for [[algorithm]]s on graphs or networks. ...

...the [[bipartite graph]] below it, where each vertex has a [[degree (graph theory)|degree]] equal to the number assigned to it.]] ...s,b_m)</math> is the [[bipartite graph|degree sequence]] of this bipartite graph. ...

...nal|last1=Friedgut|first1=Ehud|last2=Kalai|first2=Gil|title=Every monotone graph property has a sharp threshold|journal=Proceedings of the American Mathemat ...= \sum_{S \subset [n]} \widehat{f}(S) x_S, \text{ where } x_S = \prod_{i \in S} x_i. </math> ...

{{short description|Graph coloring in which every 4-vertex path uses ≥3 colors}} ...ph star coloring.svg|thumb|right|300px|The star chromatic number of [[Dyck graph]] is 4, while the chromatic number is 2.]] ...

{{Short description|Abstraction of graph shortest cycles}} ...edge connectivity of a graph, Hall sets in [[bipartite graph]]s, even sets in families of sets, and general position of point sets. It is hard to compute ...

...e degree is an odd number''. This observation means that if we are given a graph and an odd-degree vertex, and we are asked to find some other odd-degree ve ...[[Complete (complexity)|complete]] for the class PPA if in addition, this graph search problem is reducible to that problem. ...

...es are colored such that every edge has at least one vertex of each color (in this case, red and green).]] ...he Theory of NP-Completeness|Garey & Johnson's]] classical [[NP-complete]] problems.<ref name="GareyJohnson"/> The problem is sometimes called [[Property B|hyp ...

{{Short description|Graph used in computational complexity theory and graph theory}} ...^{3}</math>, formed by connecting vertices at distance two from each other in a three-dimensional cube]] ...

...versal of size 2: removing the two blue bottom vertices leaves a bipartite graph.]] ...the vertices of an odd cycle transversal from a graph leaves a [[bipartite graph]] as the remaining [[induced subgraph]].{{r|pa}} ...

...[[minimum-cost flow problem]]. The network simplex method works very well in practice, typically 200 to 300 times faster than the simplex method applied ..., but with a higher dependence on the numbers of edges and vertices in the graph, have been known for longer.<ref>{{citation ...

{{Short description|Intersection graph representing regions on the Euclidean plane}} ...left), or as the half-square of a planar bipartite graph (lower right, the graph of the [[rhombic dodecahedron]])]] ...