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A proper vertex coloring of a graph $G$ is acyclic if $G$ contains no bicolored cycle. A graph $G$ is acyclically $L$-list colorable if for a given list assignment $L=\{L(v): v\in V(G)\}$, there exists an acyclic coloring $\phi$ of $G$ such that $\phi(v)\in L(v)$ for all $v\in V(G)$. A graph $G$ is acyclically $k$-choosable if $G$ is acyclically $L$-list colorable for any list assignment with $L(v)\geq k$ for all $v\in V(G)$. Let $G$ be a planar graph without $5$-cycles and adjacent $4$-cycles. In this article, we prove that $G$ is acyclically $5$-choosable if every vertex $v$ in $G$ is incident with at most one $i$-cycle, $i\in\{6,7\}$.
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참고문헌 (18)
참고문헌 신청
J. A. Bondy / 1976 / Graph Theory with Applications / MacMillan
O. V. Borodin / 2002 / Acyclic list 7-coloring of planar graphs / J. Graph Theory 40(2):83~90
O. V. Borodin / 2011 / Acyclic 5-choosability of planar graphs without 4-cycles / Siberian Math. J. 52(3):411~425
O. V. Borodin / 2011 / Acyclic 5-choosability of planar graphs without adjacent short cycles / J. Graph Theory 68(2):169~176
O. V. Borodin / 2012 / Acyclic 4-choosability of planar graphs without adjacent short cycles / Discrete Math. 312(22):3335~3341
O. V. Borodin / 2002 / Acyclic list 7-coloring of planar graphs / J. Graph Theory 40(2):83~90
O. V. Borodin / 2011 / Acyclic 5-choosability of planar graphs without 4-cycles / Siberian Math. J. 52(3):411~425
O. V. Borodin / 2011 / Acyclic 5-choosability of planar graphs without adjacent short cycles / J. Graph Theory 68(2):169~176
O. V. Borodin / 2012 / Acyclic 4-choosability of planar graphs without adjacent short cycles / Discrete Math. 312(22):3335~3341
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