List-Coloring Claw-Free Graphs with $\Delta-1$ Colors
Copyright policy )List-Coloring Claw-Free Graphs with $\Delta-1$ Colors
We prove that if $G$ is a quasi-line graph with $��(G)>��(G)$ and $��(G)\ge 69$, then $��_{OL}(G)\le ��(G)-1$. Together with our previous work, this implies that if $G$ is a claw-free graph with $��(G)>��(G)$ and $��(G)\ge 69$, then $��_{\ell}(G)\le ��(G)-1$.
24 pages, 5 figures
- Virginia Commonwealth University United States
list coloring, Extremal problems in graph theory, Alon-Tarsi theorem, Vertex degrees, online list-coloring, kernel method, Coloring of graphs and hypergraphs, claw-free graph, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Borodin-Kostochka conjecture
list coloring, Extremal problems in graph theory, Alon-Tarsi theorem, Vertex degrees, online list-coloring, kernel method, Coloring of graphs and hypergraphs, claw-free graph, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Borodin-Kostochka conjecture
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