Choosability of the square of a planar graph with maximum degree four

Abstract

We study squares of planar graphs with the aim to determine their list chromatic number. We present new upper bounds for the square of a planar graph with maximum degree $\Delta \le 4$. In particular $G^2$ is 5-, 6-, 7-, 8-, 12-, 14-choosable if the girth of $G$ is at least 16, 11, 9, 7, 5, 3 respectively. In fact we prove more general results, in terms of maximum average degree, that imply the results above.

arXiv comment14 pages, 6 figures; fixed typo

Cited by in corpus (1)

• Relaxation of Wegner's Planar Graph Conjecture for maximum degree 4