Coloring \((P_5, \text{gem})\)-free graphs with \(\Delta -1\) colors
The Borodin-Kostochka Conjecture states that for a graph \(G\), if \(\Delta(G) \geq 9\) and \(\omega(G) \leq \Delta(G)-1\), then \(\chi(G)\leq\Delta(G) -1\). We prove the Borodin-Kostochka Conjecture for \((P_5, \text{gem})\)-free graphs, i.e., graphs with no induced \(P_5\) and no induced \(K_1\vee...
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| creator | Cranston, Daniel W Hudson Lafayette Rabern, Landon |
| description | The Borodin-Kostochka Conjecture states that for a graph \(G\), if \(\Delta(G) \geq 9\) and \(\omega(G) \leq \Delta(G)-1\), then \(\chi(G)\leq\Delta(G) -1\). We prove the Borodin-Kostochka Conjecture for \((P_5, \text{gem})\)-free graphs, i.e., graphs with no induced \(P_5\) and no induced \(K_1\vee P_4\). |
| doi_str_mv | 10.48550/arxiv.2006.02015 |
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| title | Coloring \((P_5, \text{gem})\)-free graphs with \(\Delta -1\) colors |
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