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{{short description|Undirected unit-distance graph requiring four colors}} {{infobox graph ...

...]], a '''fractional matching''' is a generalization of a [[Matching (graph theory)|matching]] in which, intuitively, each vertex may be broken into fractions Given a [[graph (discrete mathematics)|graph]] ''G'' = (''V'', ''E''), a fractional matching in ''G'' is a function that assigns, to each edge ''e'' in ''E'', ...

In [[graph theory]], '''Ryser's conjecture''' is a conjecture relating the maximum matching s ...) \leq \nu(H)</math>. This is known to be true by [[Kőnig's theorem (graph theory)|Kőnig's theorem]]. ...

{{Graph families defined by their automorphisms}} In [[graph theory|graph-theoretic mathematics]], a '''biregular graph'''<ref>{{citation ...

...url=https://faculty.math.illinois.edu/~west/openp/|title=Problems in Graph Theory and Combinatorics|website=faculty.math.illinois.edu|access-date=2019-05-05} Above ''G'' can be a [[multigraph]] (can have [[loop (graph theory)|loop]]s). ...

{{Short description|Concept in graph theory}} ...ners corresponds to a matching. It has great theoretical importance in the theory of matching.<ref name="lp">{{Cite Lovasz Plummer}}</ref>{{rp|273–285}} ...

...t same matching is definitionally the maximum-cardinality matching for the graph, but in a hypergraph, where the number of vertices connected by an edge is ...t is an extension of the notion of [[Matching (graph theory)|matching in a graph]].<ref name="lp">{{Cite Lovasz Plummer}}</ref>{{rp|466–470}} <ref>{{Cite bo ...

...tex of that set. It is an extension of the notion of [[vertex cover]] in a graph.<ref name="lp2">{{Cite Lovasz Plummer}}</ref>{{rp|466–470}}<ref>{{Cite book ...itting set''': given a collection of sets, a set which [[Intersection (set theory)|intersects]] all sets in the collection in at least one element is called ...

...g subsets), formed by the sets of vertices in the [[Independent set (graph theory)|independent sets]] of ''G''. Any subset of an independent set is itself a ...endence complex of a graph equals the [[clique complex]] of its complement graph, and vice versa. ...

...n | title=Graphs without quadrilaterals | journal=Journal of Combinatorial Theory, Series B | publisher=Elsevier BV | volume=34 | issue=2 | year=1983 | issn= ...ber of unit distances in a convex n-gon|journal=[[Journal of Combinatorial Theory]]|series=Series A|volume=55|issue=2|year=1990|pages=316–320|doi=10.1016/009 ...

'''Deficiency''' is a concept in [[graph theory]] that is used to refine various theorems related to [[perfect matching]] i ...(''V'', ''E'')}} be a graph, and let ''U'' be an [[Independent set (graph theory)|independent set]] of vertices, that is, ''U'' is a subset of ''V'' in whic ...

...urnal|last=Füredi|first=Zoltán|date=1989-05-01|title=Covering the complete graph by partitions|journal=Discrete Mathematics|language=en|volume=75|issue=1|pa It is a 2-[[Regular graph|regular hypergraph]] (each vertex is in exactly two edges), and its maximum ...

...lved|mathematics|Does the minimum number of edges in a dicut of a directed graph always equal the maximum number of disjoint dijoins?}} In the mathematics of [[directed graph]]s, '''Woodall's conjecture''' is an unproven relationship between [[dicut] ...

...boricity]] of an [[undirected graph]], the minimum number of [[tree (graph theory)|forests]] needed to cover all of its edges. Matroid partitioning may be so | contribution = 5. Fractional arboricity and matroid methods ...

...guage=en}}</ref> was an American [[mathematician]] specializing in [[graph theory]]. He spent his teaching career at [[Texas A&M University]]. ...ing in squares and higher powers of graphs, and his thesis adviser was the graph theorist [[William Thomas Tutte]]. ...

{{Short description|Special labeling in graph theory}} ...idence coloring''' is a special [[graph labeling]] where each [[Incidence (graph)|incidence]] of an edge with a vertex is assigned a color under certain con ...

# Compute an optimal fractional solution <math>x</math> to the [[linear programming relaxation]] (LP) of th # Round the fractional solution <math>x</math> of the LP to an integer solution <math>x'</math> of ...

...region allows to create the '''region automaton''', which is a [[directed graph]] in which each node is a region, and each edge <math>r\to r'</math> ensure ...te journal |last1=Alur |first1=Rajeev |last2=Dill |first2=David L |title=A theory of timed automata |journal=Theoretical Computer Science |date=April 25, 199 ...

...reto-efficient (fPO)''' if it is not Pareto-dominated by any discrete ''or fractional'' allocation.<ref name=":0">Barman, S., Krishnamurthy, S. K., & Vaish, R., ...''' is not Pareto-dominated by any allocation at all - whether discrete or fractional - then it is called '''fractionally Pareto-efficient''' (usually abbreviat ...

{{Short description|Vertex adjacent to all others in a graph}} [[File:Universal vertex.svg|thumb|A graph with a universal vertex, {{mvar|u}}]] ...