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...<math>a_{i+1} = b_i</math> for all <math> 1 \leq i \leq k-1 </math>. Shift graphs are [[Triangle-free graph|triangle-free]], and for fixed <math>k</math> the | contribution = On chromatic number of infinite graphs ...

...of pairs, where the digits represent the [[directed graph|indegree]] and [[directed graph|outdegree]] of a given vertex respectively. The problem asks whether ...]] <math>v_i</math> has [[directed graph|indegree]] <math>a_i</math> and [[directed graph|outdegree]] <math>b_i</math>. ...

A 1-graph is just the [[path category]] of a [[directed graph]]. In this case the degree map takes a path to its length. ...h>k</math>-graphs can be considered higher-dimensional analogs of directed graphs. ...

...strictions of relative movements of the objects placed in the plane. These graphs, while sharing common idea, have different definition, depending on a parti ...nt graphs is as follows. The constraint graph for a given floorplan is a [[directed graph]] with vertex set being the set of floorplan blocks and there is an e ...

{{unsolved|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 [[ ...

...a characterization analogous to the classical [[Erdős–Gallai theorem]] for graphs, but in contrast to this solution with exponentially many inequalities. In ...matics)|matrices]]. The connection can be seen if one realizes that each [[directed graph]] has an [[adjacency matrix]] where the column sums and row sums corr ...

...An <math>O(VE)</math> algorithm for ear decompositions of matching-covered graphs|journal=ACM Transactions on Algorithms|volume=1|issue=2|pages=324–337|doi=1 == Algorithms for general graphs == ...

{{short description|Directed acyclic graph with ≤1 directed paths between any two nodes}} ...ructures: a [[directed acyclic graph]] (DAG) in which there is at most one directed path between any two [[Vertex (graph theory)|vertices]], or equivalently in ...

...ub>n</sub>'',''b_n'')) the indegree-outdegree pairs of a labeled directed graph with at most one loop per vertex? ...ne Greenhill]]<ref>{{harvtxt|Greenhill|2011}}</ref> (for regular bipartite graphs with a forbidden [[Graph factorization|1-factor]]) and for [[sequence (grap ...

[[File:Conjugate-dessins.svg|thumb|Two non-isomorphic graphs realized from the degree sequence (3, 2, 2, 2, 2, 1, 1, 1).]] | title = A remark on the existence of finite graphs ...

...the '''zero-weight cycle problem''' is the problem of deciding whether a [[directed graph]] with weights on the edges (which may be positive or negative or zer ...graph]]. Therefore, the special case of the zero-weight cycle problem, on graphs with no negative cycle, has a [[polynomial time|polynomial-time]] algorithm ...

[[File:Directed graph no background.svg|upright|thumb|A simple directed graph]] ...hat is made up of a set of [[Vertex (graph theory)|vertices]] connected by directed [[Edge (graph theory)|edges]], often called '''arcs'''. ...

...ved in the worst case. Even though the algorithm is designed for connected graphs, it can be applied individually to each [[Connected component (graph theory == Graphs with weights from finite universes == ...

...raph.svg|thumb|180x180px|For comparison, the same graph plotted as [[Force-directed graph drawing|spring graph drawing]].]] '''Spectral layout''' is a class of [[algorithm]] for [[Graph drawing|drawing graphs]]. The layout uses the [[eigenvectors]] of a matrix, such as the [[Laplace ...

{{About|a notion of higher-dimensional directed graph|the forensic instrument|Polygraph|the dual pen device that produces a ...larly in [[category theory]], a '''polygraph''' is a generalisation of a [[directed graph]]. It is also known as a '''computad'''. They were introduced as "p ...

...high order must include exponentially many sets. More strongly, for these graphs, even brambles whose order is slightly larger than the square root of the t ...er of vertices in the given graph. Even faster algorithms are possible for graphs with few minimal separators.<ref>{{citation ...

...ded to the a graph when a new website is published. The movement about the graphs nodes is modeled by choosing a start node at random, then performing a shor ...<math>t</math> vertices and <math>t</math> edges. The process of defining graphs is parameterized with a probability <math>p</math>, thus we let <math>q= 1- ...

...ast1=Babai |first1=László |authorlink=László Babai|title=Spectra of Cayley graphs |journal=[[Journal of Combinatorial Theory, Series B]] |date=October 1979 | ...ath> be the [[Cayley graph]] (or [[Lovász conjecture#Directed Cayley graph|directed Cayley graph]]) corresponding to a [[Generating set of a group|generating s ...

{{Short description|Trees with additional directed half edges}} ...lossom trees can be used to [[sampling (statistics)|sample]] random planar graphs.<ref name=Albenque15>{{cite arXiv |last1= Albenque|first1= Marie|last2=Poul ...

...any of the following definitions, all of which are equivalent (for finite graphs). ...minimum of the number of edges directed clockwise and the number of edges directed counterclockwise. Define the ''imbalance'' of the oriented graph to be the ...