Results 171 to 180 of about 523,591 (296)
A Note on Extendable Sets of Colorings and Rooted Minors
Journal of Graph Theory, EarlyView.ABSTRACT DeVos and Seymour proved that for every set C $C$ of 3‐colorings of a set X $X$ of vertices, there exists a plane graph G $G$ with vertices of X $X$ incident with the outer face such that a 3‐coloring of X $X$ extends to a 3‐coloring of G $G$ if and only if it belongs to C $C$.
Zdeněk Dvořák, Jan M. Swart
wiley +1 more source
Equivalent Formulation of Thomassen's Conjecture Using Tutte Paths in Claw‐Free Graphs
Journal of Graph Theory, EarlyView.ABSTRACT We continue studying Thomassen's conjecture (every 4‐connected line graph has a Hamilton cycle) in the direction of a recently shown equivalence with Jackson's conjecture (every 2‐connected claw‐free graph has a Tutte cycle), and we extend the equivalent formulation as follows: In every connected claw‐free graph, any two vertices are connected
Adam Kabela +2 more
wiley +1 more source
Obstructions for Homomorphisms to Odd Cycles in Series‐Parallel Graphs
Journal of Graph Theory, EarlyView.ABSTRACT For a graph H $H$, an H $H$‐colouring of a graph G $G$ is a vertex mapping ϕ : V ( G ) → V ( H ) $\phi :V(G)\to V(H)$ such that adjacent vertices are mapped to adjacent vertices. A graph G $G$ is C 2 k + 1 ${C}_{2k+1}$‐critical if G $G$ has no C 2 k + 1 ${C}_{2k+1}$‐colouring but every proper subgraph of G $G$ has a C 2 k + 1 ${C}_{2k+1 ...
Eun‐Kyung Cho +3 more
wiley +1 more source
Learning-assisted theorem proving with millions of lemmas.
J Symb Comput, 2015 Kaliszyk C, Urban J.
europepmc +1 more source
A Note on Lovász Characterization of Perfect Graphs
Journal of Graph Theory, EarlyView.ABSTRACT A graph is perfect if, for every induced subgraph, the chromatic number equals the size of its largest clique. In 1972, Lovász established a fundamental characterization of perfect graphs, showing that a graph is perfect if and only if, for every induced subgraph, the product of the size of the largest independent set and the size of the ...
James Alex
wiley +1 more source
Characterization of Graphs Without Even F $F$‐Orientations
Journal of Graph Theory, EarlyView.ABSTRACT A graph G $G$ is 1‐extendable if every edge belongs to at least one 1‐factor of G $G$. Let G $G$ be a graph with a 1‐factor F $F$. Then an even (odd) F $F$ ‐orientation of G $G$ is an orientation in which each F $F$‐alternating cycle has exactly an even (odd) number of edges directed in the same fixed direction around the cycle.
Marién Abreu +3 more
wiley +1 more source
Hulls of Non-Separable Constacyclic Codes over FqR and Their Applications in Constructing New QECCs. [PDF]
Entropy (Basel)Zheng X, Kong B, Zhang E.
europepmc +1 more source
Two‐Block Paths in Oriented Graphs of Large Semidegree
Journal of Graph Theory, EarlyView.ABSTRACT We study the existence of oriented paths with two blocks in oriented graphs under semidegree conditions. A block of an oriented path is a maximal directed subpath. Given positive integers k $k$ and ℓ $\ell $ with k / 2 ≤ ℓ < k $k/2\le \ell \lt k$, we establish a semidegree function that guarantees the containment of every oriented path with ...
Irena Penev +4 more
wiley +1 more source
On the metric spaces of lattices and periodic point sets. [PDF]
J Appl Comput TopolGarber A, Virk I, Zava N.
europepmc +1 more source