A 2-assignment on a graph G (V,E) is a collection of pairs Lv of allowed colors speciยฎed for all vertices v PV. The graph G (with at least one edge) is said to have oriented choice number 2 if it admits an orientation which satisยฎes the following property: For every 2-assignment there exists a choic
List T-colorings of graphs
โ Scribed by Barry A. Tesman
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 876 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Given a finite set T of positive integers containing {0}, a T-coloring of a simple graph G is a nonnegative integer function f defined on the vertex set of G, such that if (u, v} E E(G) then Lf(u) -f (u)l $ T. The T-span of a T-coloring is defined as the difference of the largest and smallest colors
The following question was raised by Bruce Richter. Let G be a planar, 3-connected graph that is not a complete graph. Denoting by d(v) the degree of vertex v, is G L-list colorable for every list assignment L with |L(v)|=min{d(v), 6} for all v โ V (G)? More generally, we ask for which pairs (r, k)
## Abstract We prove that a 2โconnected, outerplanar bipartite graph (respectively, outerplanar nearโtriangulation) with a list of colors __L__ (__v__ ) for each vertex __v__ such that $|L(v)|\geq\min\{{\deg}(v),4\}$ (resp., $|L(v)|\geq{\min}\{{\deg}(v),5\}$) can be __L__โlistโcolored (except when
## Abstract Given an edge coloring __F__ of a graph __G__, a vertex coloring of __G__ is __adapted to F__ if no color appears at the same time on an edge and on its two endpoints. If for some integer __k__, a graph __G__ is such that given any list assignment __L__ to the vertices of __G__, with |_
Given a finite set T of positive integers, with 0 E T, a T-coloring of a graph G = (V, E) is a functionf: V -+ No such that for each {x, y} E E If(x) -f(y)l#T. The T-span is the difference between the largest and smallest colors and the T-span of G is the minimum span over all T-colorings of G. We s