Partial list colouring of certain graphs
Jeannette Janssen, Rogers Mathew, and Deepak Rajendraprasad

TL;DR
This paper investigates the partial list colouring conjecture, proving its validity for specific graph classes and providing counterexamples for a related variant, thereby advancing understanding of list colourability in graphs.
Contribution
It proves the partial list colouring conjecture for certain graph classes and constructs counterexamples for a related open question.
Findings
Partial list colouring conjecture holds for claw-free, large chromatic number, chordless, and series-parallel graphs.
Counterexamples show the related question does not always hold.
Explicit construction of 3-choosable graphs with small 2-choosable induced subgraphs.
Abstract
Let be a graph on vertices and let be an arbitrary function that assigns each vertex in a list of colours. Then is -list colourable if there exists a proper colouring of the vertices of such that every vertex is coloured with a colour from its own list. We say is -choosable if for every such function , is -list colourable. The minimum such that is -choosable is called the list chromatic number of and is denoted by . Let and let be a positive integer less than . The partial list colouring conjecture due to Albertson et al. \cite{albertson2000partial} states that for every that maps the vertices of to -sized lists, there always exists an induced subgraph of of size at least that is -list…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research
