Abstract
In this paper we prove that every planar graph $G$ is 3-choosable if it contains no cycle of length at most 10 with a chord. This generalizes a result obtained by Borodin [J. Graph Theory 21(1996) 183-186] and Sanders and Zhao [Graphs Combin. 11(1995) 91-94], which says that every planar graph $G$ without $k$-cycles for all $4 \leq k \leq 9$ is 3-colorable.
Citation
Wei-Fan Wang. "PLANAR GRAPHS THAT HAVE NO SHORT CYCLES WITH A CHORD ARE 3-CHOOSABLE." Taiwanese J. Math. 11 (1) 179 - 186, 2007. https://doi.org/10.11650/twjm/1500404644
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