On $k$-colorability of $(bull, H)$-free graphs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912566072049664 |
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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 $3$-colorability problem is a well-known NP-complete problem and it remains NP-complete for $bull$-free graphs, where a $bull$ is the graph consisting of a $K_3$ with two pendant edges attached to two of its vertices. In this paper, for $k\geq3$, we characterize all $k$-colorable $(bull,claw)$-free graphs containing an induced cycle of length at least $6$. Moreover, we present the full characterization of all non $4$-colorable connected $(bull,claw)$-free graphs and $(bull,chair, C_5)$-free graphs, and all non $5$-colorable connected $(bull, claw, C_5)$-free graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $k$-colorability of $(bull, H)$-free graphs Hodur, Nadzieja Pilśniak, Monika Prorok, Magdalena Schiermeyer, Ingo Combinatorics The $3$-colorability problem is a well-known NP-complete problem and it remains NP-complete for $bull$-free graphs, where a $bull$ is the graph consisting of a $K_3$ with two pendant edges attached to two of its vertices. In this paper, for $k\geq3$, we characterize all $k$-colorable $(bull,claw)$-free graphs containing an induced cycle of length at least $6$. Moreover, we present the full characterization of all non $4$-colorable connected $(bull,claw)$-free graphs and $(bull,chair, C_5)$-free graphs, and all non $5$-colorable connected $(bull, claw, C_5)$-free graphs. |
| title | On $k$-colorability of $(bull, H)$-free graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.01698 |