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

Autor:	Lu, Huajing, Zhu, Xuding
Rok vydání:	2019
Předmět:	Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	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 $AT(G-M)\leq 3$. This implies that every planar graph without 4-cycles and $l$-cycles for some $l\in\{5, 6, 7\}$ is 1-defective 3-paintable. Comment: 16 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1910.12598 Zobrazit plný text záznamu View this record from Arxiv