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{{short description|Conjecture in group theory}} ...the length of any [[orbit (group theory)|orbit]] of <math>G_\alpha</math> in the set <math>S \setminus \{\alpha\}</math>. ...

..., discovered by [[Julius Petersen]], is one of the earliest works in graph theory. It can be stated as follows:{{r|lovasz}} Let <math>G</math> be a [[regular graph]] whose [[Degree (graph theory)|degree]] is an even number, <math>2k</math>. Then the edges of <math>G</ma ...

{{short description|Sufficient condition for a Hamiltonian cycle in a graph, based on its vertex's degrees}} ...a]], a protégé of [[Paul Erdős]] born in 1947, who discovered this theorem in 1962. ...

...chnical tool for studying stable maps. Since then it has proved important in its own right. Roughly speaking, two map germs ''&fnof;'',&nbsp;''g'' are ...is equivalence is measuring the contact between the graph of ''f'' and the graph of the zero map. ...

{{Short description|Refinement of perfect matching theorems}} ...e journal|last=Ore|first=Oystein|date=1955-12-01|title=Graphs and matching theorems|url=https://projecteuclid.org/euclid.dmj/1077466548|journal=Duke Mathematic ...

...te book|title=Fixed Point Theorems with Applications to Economics and Game Theory|last=Border|first=Kim C.|publisher=Cambridge University Press|year=1989|isb : <math>\forall x \in X: \,\,\, f(x) \in F(x) \,.</math> ...

...Annabell Berger: ''A Note on the Characterization of Digraphic Sequences'' In: ''Discrete Mathematics'', 2014, pp. 38–41</ref> reinvented this result and ...atrices]]. The connection can be seen if one realizes that each [[directed graph]] has an [[adjacency matrix]] where the column sums and row sums correspond ...

...s. It is named after [[Brian Alspach]], who posed it as a research problem in 1981. A [[mathematical proof|proof]] was published by {{harvs|first1=Darryn ...ber of cycles that include that vertex, an even number. And for the cycles in a disjoint cycle cover to have a given collection of lengths, ...

...by [[Joseph O'Rourke (professor)|Joseph O'Rourke]], and published in 1987 in the International Series of Monographs on Computer Science of the [[Oxford ...th <math>n</math> corners, but a simplified proof by Steve Fisk based on [[graph coloring]] and [[polygon triangulation]] is more widely known. This is the ...

[[File:Triakisicosahedron.jpg|thumb|The [[triakis icosahedron]], a polyhedron in which every edge has endpoints with total degree at least 13]] ...total of at most 13 sides.{{r|k}} It was named and popularized in the west in the 1970s by [[Branko Grünbaum]].{{r|g1|g2}} ...

...) is a British mathematician specializing in [[combinatorics]] and [[graph theory]]. His current positions are as [[emeritus]] professor of Combinatorial Mat ...~smshiltn/ Personal Homepage]</ref> His dissertation was "Representation Theorems for Integers and Real Numbers" under his advisor David E. Daykin.<ref name= ...

[[File:Complete-edge-coloring.svg|thumb|A partition of a [[complete graph]] on 8 vertices into 7 colors ([[perfect matching]]s), the case ''r''&nbsp; ...by and named after [[Zsolt Baranyai]]) deals with the [[Glossary of graph theory#Independence|decompositions]] of complete [[hypergraph]]s. ...

....svg|thumb|{{math|''K''₅}} subdivision of the 12-vertex [[crown graph]]]] ...to 1984.</ref> A proof was announced in 2016, and published in four papers in 2020. ...

...ng [[longest path problem|longest paths]] and [[graph coloring|colorings]] in graphs, and to the [[Erdős–Szekeres theorem]] on monotonic subsequences. ...l order|totally ordered]] subset of the given partial order. For instance, in the set of positive integers from 1 to ''N'', ordered by [[divisibility]], ...

...matics)|knot]]s or [[link (knot theory)|link]]s. The conditions are stated in terms of the [[group (mathematics)|group]] structures on braids. ...ates that every [[knot (mathematics)|knot]] or [[link (knot theory)|link]] in three-dimensional Euclidean space is the closure of a [[braid (mathematics) ...

{{short description|Classifies quivers (multigraphs) of finite type in terms of Dynkin diagrams.}} ...Gabriel]], classifies the [[quiver (mathematics)|quivers]] of finite type in terms of [[Dynkin diagram]]s. ...

...allai theorem]] for simple graphs. The theorem was published independently in 1957 by [[H. J. Ryser]] and [[David Gale]]. ...um_{i=1}^{n}b_i</math> and the following inequality holds for all <math>k \in \{1, \ldots, n\}</math>: ...

...m''' is a result of [[Paul Erdős]] according to which an {{mvar|n}}-vertex graph that does not have a simple cycle of length {{math|2''k''}} can only have { The result was stated without proof by Erdős in 1964.<ref>{{citation ...

...[clique (graph theory)|clique]] with the same [[cardinality]] as the whole graph.{{r|milpou}} ...assistance in its proof. They applied these results to the [[comparability graph]]s of [[partially ordered set]]s to show that each partial order contains e ...

...ize [[Leavitt algebra]]s and may be considered as algebraic analogues of [[graph C*-algebras]]. Leavitt path algebras were simultaneously introduced in 2005 by [[Gene Abrams]] and Gonzalo Aranda Pino<ref>Abrams, Gene; Aranda Pi ...