# choosability

## Choosability of Graph Powers ★★

Author(s): Noel

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

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

Author(s):

Question   What is the choice number of for general ?

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

Author(s): Noel

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

## 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 . 