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...tain upper bounds for the number of [[perfect matching]]s in a [[bipartite graph]]. ...ath> of size <math>n</math> with row sums <math>r_i = a_{i1} + \cdots + a_{in}</math> for <math>i=1, \ldots , n</math> can be estimated by ...

...which a program instruction executes if the previous instruction evaluates in a way that allows its execution. ...tion A if the outcome of A determines whether B should be executed or not. In the following example, the instruction <math>S_2</math> has a control depen ...

...heorem in graph theory describing number of edge-disjoint spanning trees a graph can have}} ...[spanning tree]]s (and more generally [[Forest (graph theory)|forests]]) a graph can have: ...

[[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}} ...

....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. ...

...hresholds |eprint=math/0603218 }}</ref> It was proven in a paper published in 2024.<ref name=pp24/> ...h edge is included with probability <math>p</math>, it is unlikely for the graph to contain a [[Hamiltonian cycle]] if <math>p</math> is less than a thresho ...

{{Short description|Formula in graph theory}} In [[graph theory]], a '''deletion-contraction formula / recursion''' is any formula of the f ...

...he first graph is connected by exactly one path of length 1, and each pair in the second is connected by one of length 2. These are the cases <math>k = 1 {{unsolved|mathematics|Is there a finite graph on at least two vertices in which each pair of distinct vertices is connected by ''exactly one'' path o ...

{{Short description|Graphoid math statements}} {{about|the use in logic and probability|the use in matroid theory|Matroid}} ...

{{Short description|On Hamiltonian cycles in planar graphs}} [[File:Grinberg 5CEC Nonhamiltonian graph.svg|thumb|A graph that can be proven non-Hamiltonian using Grinberg's theorem]] ...

{{Short description|System of arithmetic in proof theory}} ...ey Friedman's Research on the Foundations of Mathematics'' (1985), Studies in Logic and the Foundations of Mathematics vol. 117.</ref> is the system of a ...

{{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}} ...

...lemma provides a similar yet more general notion on the space of graphons, in which a scalar of the cut distance between two graphs is correlated to the == Graph embedding version of counting lemma == ...

{{Short description|Every triangle-free planar graph is 3-colorable}} [[File:Groetsch-3-coloring.svg|thumb|A 3-coloring of a triangle-free planar graph]] ...

...ecture relating the maximum matching size and the minimum transversal size in [[hypergraph]]s. This conjecture first appeared in 1971 in the Ph.D. thesis of J. R. Henderson, whose advisor was [[H. J. Ryser|Herber ...

In [[network science]], a '''sparse network''' has ''much fewer'' links than t ...networks are indeed sparse. There is, however, a formal sense of sparsity in the case of infinite network models, determined by the behavior of the numb ...

...usly studied independently. Among other benefits, this provides a context in which one can formulate [[theorem]]s that apply simultaneously to all of th ...has particular properties, describe the lattice of ideals, and compute [[K-theory|K-theoretic]] invariants. ...

{{Short description|Mathematical method in extremal graph theory}} ...ity lemma and the associated counting lemma. It is a generalization of the graph regularity method, which refers to the use of [[Szemerédi regularity lemma| ...

...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 ...

...e=1927ZaMM....7...58P|issn=1521-4001}}</ref> and later by [[Gerard Laman]] in 1970.<ref name=":1">{{Cite journal|last=Laman|first=G.|date=1970-10-01|titl ...th>G=(V,E)</math> is [[Structural rigidity#Definitions|generically rigid]] in <math>2</math>-dimensions with respect to bar-joint frameworks if and only ...