27 research outputs found
Beyond Ohba's Conjecture: A bound on the choice number of -chromatic graphs with vertices
Let denote the choice number of a graph (also called "list
chromatic number" or "choosability" of ). Noel, Reed, and Wu proved the
conjecture of Ohba that when . We
extend this to a general upper bound: . Our result is sharp for
using Ohba's examples, and it improves the best-known
upper bound for .Comment: 14 page
Every Elementary Graph is Chromatic Choosable
Elementary graphs are graphs whose edges can be colored using two colors in
such a way that the edges in any induced get distinct colors. They
constitute a subclass of the class of claw-free perfect graphs. In this paper,
we show that for any elementary graph, its list chromatic number and chromatic
number are equal
A Proof of a Conjecture of Ohba
We prove a conjecture of Ohba which says that every graph on at most
vertices satisfies .Comment: 21 page