On graphs with chromatic number and maximum degree both equal to nine
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909294009516032 |
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| author | Galindo, Rachel McDonald, Jessica |
| author_facet | Galindo, Rachel McDonald, Jessica |
| contents | An equivalent version of the Borodin-Kostochka Conjecture, due to Cranston and Rabern, says that any graph with $χ= Δ= 9$ contains $K_3 \lor E_6$ as a subgraph. Here we prove several results in support of this conjecture, where vertex-criticality and forbidden substructure conditions get us either close or all the way to containing $K_3 \lor E_6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On graphs with chromatic number and maximum degree both equal to nine Galindo, Rachel McDonald, Jessica Combinatorics An equivalent version of the Borodin-Kostochka Conjecture, due to Cranston and Rabern, says that any graph with $χ= Δ= 9$ contains $K_3 \lor E_6$ as a subgraph. Here we prove several results in support of this conjecture, where vertex-criticality and forbidden substructure conditions get us either close or all the way to containing $K_3 \lor E_6$. |
| title | On graphs with chromatic number and maximum degree both equal to nine |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.12693 |