On 3-colourability of $(bull, H)$-free graphs
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914761365520384 |
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| author | Hodur, Nadzieja Pilśniak, Monika Prorok, Magdalena Schiermeyer, Ingo |
| author_facet | Hodur, Nadzieja Pilśniak, Monika Prorok, Magdalena Schiermeyer, Ingo |
| contents | The $3$-colourability problem is a well-known NP-complete problem and it remains NP-complete for $bull$-free graphs, where $bull$ is the graph consisting of $K_3$ with two pendant edges attached to two of its vertices. In this paper we study $3$-colourability of $(bull,H)$-free graphs for several graphs $H$. We show that these graphs are $3$-colourable or contain an induced odd wheel $W_{2p+1}$ for some $p\geq 2$ or a spindle graph $M_{3p+1}$ for some $p\geq 1$. Moreover, for all our results we can provide certifying algorithms that run in polynomial time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12515 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On 3-colourability of $(bull, H)$-free graphs Hodur, Nadzieja Pilśniak, Monika Prorok, Magdalena Schiermeyer, Ingo Combinatorics The $3$-colourability problem is a well-known NP-complete problem and it remains NP-complete for $bull$-free graphs, where $bull$ is the graph consisting of $K_3$ with two pendant edges attached to two of its vertices. In this paper we study $3$-colourability of $(bull,H)$-free graphs for several graphs $H$. We show that these graphs are $3$-colourable or contain an induced odd wheel $W_{2p+1}$ for some $p\geq 2$ or a spindle graph $M_{3p+1}$ for some $p\geq 1$. Moreover, for all our results we can provide certifying algorithms that run in polynomial time. |
| title | On 3-colourability of $(bull, H)$-free graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.12515 |