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- W2743756977 abstract "Abstract In 1998, Reed conjectured that every graph of maximum degree Δ and clique number ω can be colored with ⌈ 1 2 ( Δ + 1 + ω ) ⌉ colors, significantly strengthening Brooks' Theorem. As evidence for his conjecture, he proved that this is true instead when the number of colors is some nontrivial convex combination of Δ + 1 and ω. I 1979, Erdős, Rubin, and Taylor proved that a connected graph G is L-colorable for every list-assignment L satisfying | L ( v ) | ≥ d ( v ) for all v ∈ V ( G ) , unless every block of G is a clique or odd cycle. We ask if every graph G is L-colorable for every list-assignment L satisfying | L ( v ) | ≥ ⌈ 1 2 ( d ( v ) + 1 + ω ( v ) ) ⌉ , where ω ( v ) denotes the size of the largest clique in G containing v. We prove that this is true instead when | L ( v ) | is some nontrivial convex combination of d ( v ) + 1 and ω ( v ) , under certain mild assumptions." @default.
- W2743756977 created "2017-08-17" @default.
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- W2743756977 date "2017-08-01" @default.
- W2743756977 modified "2023-09-24" @default.
- W2743756977 title "A Local Epsilon Version of Reed's Conjecture" @default.
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- W2743756977 doi "https://doi.org/10.1016/j.endm.2017.07.028" @default.
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