# list coloring

## List Colourings of Complete Multipartite Graphs with 2 Big Parts ★★

Author(s): Allagan

Question   Given , what is the smallest integer such that ?

## List Total Colouring Conjecture ★★

Author(s): Borodin; Kostochka; Woodall

Conjecture   If is the total graph of a multigraph, then .

Keywords: list coloring; Total coloring; total graphs

## 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 .

## Ohba's Conjecture ★★

Author(s): Ohba

Conjecture   If , then .

## Partial List Coloring ★★★

Let be a simple graph, and for every list assignment let be the maximum number of vertices of which are colorable with respect to . Define , where the minimum is taken over all list assignments with for all .

Conjecture    Let be a graph with list chromatic number and . Then Keywords: list assignment; list coloring

## Partial List Coloring ★★★

Author(s): Albertson; Grossman; Haas

Conjecture   Let be a simple graph with vertices and list chromatic number . Suppose that and each vertex of is assigned a list of colors. Then at least vertices of can be colored from these lists.

Keywords: list assignment; list coloring

## List colorings of edge-critical graphs ★★

Author(s): Mohar

Conjecture   Suppose that is a -edge-critical graph. Suppose that for each edge of , there is a list of colors. Then is -edge-colorable unless all lists are equal to each other.

Keywords: edge-coloring; list coloring 