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- W2170818744 abstract "Let H be the graph obtained from a 6-cycle C 6 by adding an edge which joins a pair of two vertices with distance two. We show that if a planar graph does not contain H , then G is edge-t -choosable, where t = 7 if Δ (G ) = 5, and t = Δ (G ) + 1, otherwise. This extends the known results that a planar graph is edge-(Δ (G ) + 1)-choosable when Δ (G ) *** 7 and G does not contain a k -cycle for some k *** {3, 5, 6}. It is well-known that {3, 5, 6} are only integers for which the lack of a cycle of length in {3, 5, 6} for a planar graph G implies 3-degeneracy of G . As a by-product, we prove that if a planar graph G contains at most seven 3-cycles, G is 3-degenerate. We also answer a problem of Raspaud and Wang (European J. Combin. 29(2008) 1064-1075) in negative." @default.
- W2170818744 created "2016-06-24" @default.
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- W2170818744 date "2009-01-01" @default.
- W2170818744 modified "2023-09-26" @default.
- W2170818744 title "A Note on Edge Choosability and Degeneracy of Planar Graphs" @default.
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- W2170818744 doi "https://doi.org/10.1007/978-3-642-02026-1_23" @default.
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