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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2410.18309 |
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| _version_ | 1866909374214045696 |
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| author | Kabela, Adam Ryjáček, Zdeněk Skyvová, Mária Vrána, Petr |
| author_facet | Kabela, Adam Ryjáček, Zdeněk Skyvová, Mária Vrána, Petr |
| contents | We show that every $3$-connected $\{K_{1,3},Γ_3\}$-free graph is Hamilton-connected, where $Γ_3$ is the graph obtained by joining two vertex-disjoint triangles with a path of length $3$. This resolves one of the two last open cases in the characterization of pairs of connected forbidden subgraphs implying Hamilton-connectedness. The proof is based on a new closure technique, developed in a previous paper, and on a structural analysis of small subgraphs, cycles and paths in line graphs of multigraphs. The most technical steps of the analysis are computer-assisted.
Keywords: Hamilton-connected; closure; forbidden subgraph; claw-free; $Γ_3$-free |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18309 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Every $3$-connected $\{K_{1,3},Γ_3\}$-free graph is Hamilton-connected Kabela, Adam Ryjáček, Zdeněk Skyvová, Mária Vrána, Petr Combinatorics We show that every $3$-connected $\{K_{1,3},Γ_3\}$-free graph is Hamilton-connected, where $Γ_3$ is the graph obtained by joining two vertex-disjoint triangles with a path of length $3$. This resolves one of the two last open cases in the characterization of pairs of connected forbidden subgraphs implying Hamilton-connectedness. The proof is based on a new closure technique, developed in a previous paper, and on a structural analysis of small subgraphs, cycles and paths in line graphs of multigraphs. The most technical steps of the analysis are computer-assisted. Keywords: Hamilton-connected; closure; forbidden subgraph; claw-free; $Γ_3$-free |
| title | Every $3$-connected $\{K_{1,3},Γ_3\}$-free graph is Hamilton-connected |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.18309 |