List Colouring Big Graphs On-Line
Martin Derka, Alejandro L\'opez-Ortiz, Daniela Maftuleac
TL;DR
This paper explores online graph list coloring, proving the on-line version of Ohba's conjecture for planar graphs and examining various models of online list coloring.
Contribution
It establishes the validity of the on-line Ohba's conjecture for planar graphs and analyzes multiple online list coloring models.
Findings
On-line Ohba's conjecture holds for planar graphs
Several online list coloring models are examined
Results extend understanding of graph paintability in online settings
Abstract
In this paper, we investigate the problem of graph list colouring in the on-line setting. We provide several results on paintability of graphs in the model introduced by Schauz [13] and Zhu [20]. We prove that the on-line version of Ohba's conjecture is true in the class of planar graphs. We also consider several alternate on-line list colouring models.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · semigroups and automata theory