The Alon-Tarsi number of planar graphs without cycles of lengths $4$ and $l$

Abstract

This paper proves that if $G$ is a planar graph without 4-cycles and $l$-cycles for some $l\in \{5,6,7\}$, then there exists a matching $M$ such that $AT(G-M)\le 3$. This implies that every planar graph without 4-cycles and $l$-cycles for some $l\in \{5,6,7\}$ is 1-defective 3-paintable.

16 pages, 4 figures

References in corpus (1)

• The Alon-Tarsi number of subgraphs of a planar graph