Flexibility of planar graphs without $C_4$ and $C_5$

Abstract

Let $G$ be a $\{C_4,C_5\}$-free planar graph with a list assignment $L$. Suppose a preferred color is given for some of the vertices. We prove that if all lists have size at least four, then there exists an $L$-coloring respecting at least a constant fraction of the preferences.

26 pages, 6 figures. arXiv admin note: text overlap with arXiv:1902.02971 by other authors