Results 161 to 170 of about 523,591 (296)
Flexible List Coloring of Graphs With Maximum Average Degree Less Than 3
Journal of Graph Theory, EarlyView.ABSTRACT In the flexible list coloring problem, we consider a graph G $G$ and a color list assignment L $L$ on G $G$, as well as a subset U ⊆ V ( G ) $U\subseteq V(G)$ for which each u ∈ U $u\in U$ has a preferred color p ( u ) ∈ L ( u ) $p(u)\in L(u)$. Our goal is to find a proper L $L$‐coloring ϕ $\phi $ of G $G$ such that ϕ ( u ) = p ( u ) $\phi (u)=
Richard Bi, Peter Bradshaw
wiley +1 more source
Sparse Graphs With Local Covering Conditions on Edges
Journal of Graph Theory, EarlyView.ABSTRACT In 1988, Erdős suggested the question of minimizing the number of edges in a connected n $n$‐vertex graph where every edge is contained in a triangle. Shortly after, Catlin, Grossman, Hobbs, and Lai resolved this in a stronger form. In this paper, we study a natural generalization of the question of Erdős in which we replace “triangle” with ...
Debsoumya Chakraborti +3 more
wiley +1 more source
4th International Workshop on First-Order Theorem Proving- FTP'2003
, 2003 Ouvrage (éditeur).Proceedings of the 4th international workshop on first-order theorem proving. FTP'2003 is the fourth in a series of workshops intended to focus effort on First-Order Theorem Proving as a core theme of Automated Deduction, and to provide
Vigneron, Laurent, Dahn, Ingo
core
The Strong Nash‐Williams Orientation Theorem for Rayless Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In 1960, Nash‐Williams proved his strong orientation theorem that every finite graph has an orientation in which the number of arc‐disjoint directed paths between any two vertices is at least half the number of undirected edge‐disjoint paths between them (rounded down).
Max Pitz, Jacob Stegemann
wiley +1 more source
Path Degeneracy and Applications
Journal of Graph Theory, EarlyView.ABSTRACT In this work, we relate girth and path‐degeneracy in classes with sub‐exponential expansion, with explicit bounds for classes with polynomial expansion and proper minor‐closed classes that are tight up to a constant factor (and tight up to second order terms if a classical conjecture on existence of g $g$‐cages is verified). As an application,
Yuquan Lin, Patrice Ossona de Mendez
wiley +1 more source
Line Graphs of Multigraphs and the Forbidden Graph E 6
Journal of Graph Theory, EarlyView.ABSTRACT The line graph Γ of a multigraph Δ is the graph whose vertices are the edges of Δ, where two such edges are adjacent if and only if they meet in a single vertex of Δ. We provide several characterizations of such line graphs and in particular show that a graph is a line graph if and only if it does not contain one of the 32 graphs, all of which
Hans Cuypers
wiley +1 more source
Saturated Partial Embeddings of Planar Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In this work, we study how far one can deviate from optimal behavior when embedding a planar graph. For a planar graph G $G$, we say that a plane subgraph H ⊆ G $H\subseteq G$ is a plane‐saturated subgraph if adding any edge (possibly with new vertices) to H $H$ would either violate planarity or make the resulting graph no longer a subgraph of
Alexander Clifton, Nika Salia
wiley +1 more source