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
Near-optimal list colorings
โ Scribed by Michael Molloy; Bruce Reed
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 223 KB
- Volume
- 17
- Category
- Article
- ISSN
- 1042-9832
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this article we discuss the current results on the list chromatic conjecture and prove that if G is a triangle free graph with maximum degree A then xi(G) 5 9A/5. If the term "a classic" can be used about a mathematical problem less than 10 years old, then surely the following question by Jeff D
## Abstract The measurable list chromatic number of a graph __G__ is the smallest number ฮพ such that if each vertex __v__ of __G__ is assigned a set __L__(__v__) of measure ฮพ in a fixed atomless measure space, then there exist sets $c(v)\subseteq L(v)$ such that each __c__(__v__) has measure one an
## Abstract Given a __list of boxes L__ for a graph __G__ (each vertex is assigned a finite set of colors that we call a box), we denote by __f__(__G, L__) the number of Lโ__colorings__ of __G__ (each vertex must be colored wiht a color of its box). In the case where all the boxes are identical and
Let G be an n-vertex graph with list-chromatic number ฯ . Suppose that each vertex of G is assigned a list of t colors. Albertson, Grossman, and Haas [1] conjecture that at least t n /ฯ vertices can be colored from these lists. We prove a lower bound for the number of colorable vertices. As a coroll
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)