Coloring \((P_5, \text{gem})\)-free graphs with \(\Delta -1\) colors

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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Veröffentlicht in:arXiv.org 2020-06
Hauptverfasser: Cranston, Daniel W, Hudson Lafayette, Rabern, Landon
Format: Artikel
Sprache:eng
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Zusammenfassung: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 \(K_1\vee P_4\).
ISSN:2331-8422
DOI:10.48550/arxiv.2006.02015