eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
31:1
31:15
10.4230/LIPIcs.ISAAC.2020.31
article
Flexible List Colorings in Graphs with Special Degeneracy Conditions
Bradshaw, Peter
1
https://orcid.org/0000-0003-2562-6141
Masařk, Tomáš
1
https://orcid.org/0000-0001-8524-4036
Stacho, Ladislav
1
Simon Fraser University, Burnaby, Canada
For a given ε > 0, we say that a graph G is ε-flexibly k-choosable if the following holds: for any assignment L of lists of size k on V(G), if a preferred color is requested at any set R of vertices, then at least ε |R| of these requests are satisfied by some L-coloring. We consider flexible list colorings in several graph classes with certain degeneracy conditions. We characterize the graphs of maximum degree Δ that are ε-flexibly Δ-choosable for some ε = ε(Δ) > 0, which answers a question of Dvořák, Norin, and Postle [List coloring with requests, JGT 2019]. We also show that graphs of treewidth 2 are 1/3-flexibly 3-choosable, answering a question of Choi et al. [arXiv 2020], and we give conditions for list assignments by which graphs of treewidth k are 1/(k+1)-flexibly (k+1)-choosable. We show furthermore that graphs of treedepth k are 1/k-flexibly k-choosable. Finally, we introduce a notion of flexible degeneracy, which strengthens flexible choosability, and we show that apart from a well-understood class of exceptions, 3-connected non-regular graphs of maximum degree Δ are flexibly (Δ - 1)-degenerate.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol181-isaac2020/LIPIcs.ISAAC.2020.31/LIPIcs.ISAAC.2020.31.pdf
Flexibility
List Coloring
Choosability
Degeneracy