On graphs without four-vertex induced subgraphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913813767389184 |
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| author | Cameron, Kathie Hoàng, Chính T. LaGrange, Taite |
| author_facet | Cameron, Kathie Hoàng, Chính T. LaGrange, Taite |
| contents | Given a family F of graphs, a graph G is F-free if it does not contain any graph in F as an induced subgraph. The problem of determining the complexity of colouring (claw, 4K1)- free graphs is a well-known open problem. In this paper we solve the colouring problem for a subclass of (claw, 4K1)-free graphs. We design a polynomial-time algorithm to colour (claw, 4K1, bridge, C4-twin)-free graphs. This algorithm is derived from a structural theorem on (claw, 4K1, bridge, C4-twin)-free graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On graphs without four-vertex induced subgraphs Cameron, Kathie Hoàng, Chính T. LaGrange, Taite Combinatorics 05C15 G.2.2 Given a family F of graphs, a graph G is F-free if it does not contain any graph in F as an induced subgraph. The problem of determining the complexity of colouring (claw, 4K1)- free graphs is a well-known open problem. In this paper we solve the colouring problem for a subclass of (claw, 4K1)-free graphs. We design a polynomial-time algorithm to colour (claw, 4K1, bridge, C4-twin)-free graphs. This algorithm is derived from a structural theorem on (claw, 4K1, bridge, C4-twin)-free graphs. |
| title | On graphs without four-vertex induced subgraphs |
| topic | Combinatorics 05C15 G.2.2 |
| url | https://arxiv.org/abs/2505.00202 |