Partial List Colouring of Certain Graphs
Reads0
Chats0
TLDR
The partial list colouring conjecture due to Albertson, Grossman, and Haas as mentioned in this paper holds true for certain classes of graphs like claw-free graphs, chordless graphs, and series-parallel graphs.Abstract:
The partial list colouring conjecture due to Albertson, Grossman, and Haas (2000) states that for every $s$-choosable graph $G$ and every assignment of lists of size $t$, $1 \leq t \leq s$, to the vertices of $G$ there is an induced subgraph of $G$ on at least $\frac{t|V(G)|}{s}$ vertices which can be properly coloured from these lists. In this paper, we show that the partial list colouring conjecture holds true for certain classes of graphs like claw-free graphs, graphs with chromatic number at least $\frac{|V(G)|-1}{2}$, chordless graphs, and series-parallel graphs.read more
Citations
More filters
Journal ArticleDOI
Partial DP-coloring of graphs
TL;DR: In this paper, a generalization of the partial list coloring conjecture, called correspondence coloring, was introduced. But this conjecture does not hold for partial coloring of a graph with a complete graph.
Posted Content
Partial DP-Coloring
TL;DR: In this paper, the authors studied partial coloring for DP-coloring, a recent insightful generalization of list coloring introduced in 2015 by Dvořak and Postle.
Book ChapterDOI
List Colouring and Partial List Colouring of Graphs On-line
TL;DR: It is shown that the conjecture for partial list colouring on-line holds for several graph classes, namely claw-free graphs, maximal planar graphs, series-parallel graphs, and chordal graphs.
References
More filters
Journal ArticleDOI
On minimal blocks
Journal IssueDOI
On chromatic-choosable graphs
TL;DR: A graph is chromatic-choosable if its choice number coincides with its chromatic number as discussed by the authors, i.e., the number of vertices in a graph is close enough to the number in the graph to be chromatic.
Journal ArticleDOI
A Proof of a Conjecture of Ohba
TL;DR: It is proved that every graph G on at most 2i¾?G+1 vertices satisfies i-G=i-G, where i is the number of vertices of the graph and G is its diagonal.
Journal ArticleDOI
Partial list colorings
TL;DR: It is shown that if G is χ -colorable (rather than being s -choosable), then more than (1−((χ−1)/χ) t )n of the vertices of G can be colored from the lists and that this is asymptotically best possible.