The Alon-Tarsi number of planar graphs without cycles of lengths $4$ and $l$
Autor: | Lu, Huajing, Zhu, Xuding |
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Rok vydání: | 2019 |
Předmět: | |
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: |