Coloring $(P_5, \text{gem})$-free graphs with $Δ-1$ colors
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929615685025792 |
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| author | Cranston, Daniel W. Lafayette, Hudson Rabern, Landon |
| author_facet | Cranston, Daniel W. Lafayette, Hudson Rabern, Landon |
| contents | The Borodin-Kostochka Conjecture states that for a graph $G$, if $Δ(G) \geq 9$ and $ω(G) \leq Δ(G)-1$, then $χ(G)\leqΔ(G) -1$. We prove the Borodin-Kostochka Conjecture for $(P_5, \text{gem})$-free graphs, i.e., graphs with no induced $P_5$ and no induced $K_1\vee P_4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_02015 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Coloring $(P_5, \text{gem})$-free graphs with $Δ-1$ colors Cranston, Daniel W. Lafayette, Hudson Rabern, Landon Combinatorics 05C15 The Borodin-Kostochka Conjecture states that for a graph $G$, if $Δ(G) \geq 9$ and $ω(G) \leq Δ(G)-1$, then $χ(G)\leqΔ(G) -1$. We prove the Borodin-Kostochka Conjecture for $(P_5, \text{gem})$-free graphs, i.e., graphs with no induced $P_5$ and no induced $K_1\vee P_4$. |
| title | Coloring $(P_5, \text{gem})$-free graphs with $Δ-1$ colors |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2006.02015 |