# choosability

## Choosability of Graph Powers ★★

Author(s): Noel

**Question (Noel, 2013)**Does there exist a function such that for every graph ,

Keywords: choosability; chromatic number; list coloring; square of a graph

## Bounding the on-line choice number in terms of the choice number ★★

Author(s): Zhu

**Question**Are there graphs for which is arbitrarily large?

Keywords: choosability; list coloring; on-line choosability

## Choice number of complete multipartite graphs with parts of size 4 ★

Author(s):

**Question**What is the choice number of for general ?

Keywords: choosability; complete multipartite graph; list coloring

## Choice Number of k-Chromatic Graphs of Bounded Order ★★

Author(s): Noel

**Conjecture**If is a -chromatic graph on at most vertices, then .

Keywords: choosability; complete multipartite graph; list coloring

## Circular choosability of planar graphs ★

Author(s): Mohar

Let be a graph. If and are two integers, a -colouring of is a function from to such that for each edge . Given a list assignment of , i.e.~a mapping that assigns to every vertex a set of non-negative integers, an -colouring of is a mapping such that for every . A list assignment is a --list-assignment if and for each vertex . Given such a list assignment , the graph G is --colourable if there exists a --colouring , i.e. is both a -colouring and an -colouring. For any real number , the graph is --choosable if it is --colourable for every --list-assignment . Last, is circularly -choosable if it is --choosable for any , . The circular choosability (or circular list chromatic number or circular choice number) of G is

**Problem**What is the best upper bound on circular choosability for planar graphs?

Keywords: choosability; circular colouring; planar graphs

## Ohba's Conjecture ★★

Author(s): Ohba

**Conjecture**If , then .

Keywords: choosability; chromatic number; complete multipartite graph; list coloring