On 2-bisections and monochromatic edges in claw-free cubic multigraphs
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866908847698870272 |
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| author | Romaniello, Federico |
| author_facet | Romaniello, Federico |
| contents | A $k$-bisection of a multigraph $G$ is a partition of its vertex set into two parts of the same cardinality such that every component of each part has at most $k$ vertices. Cui and Liu shown that every claw-free cubic multigraph contains a $2$-bisection, while Eom and Ozeki constructed specific $2$-bisections with bounded number of monochromatic edges. Their bound is the best possible for claw-free cubic simple graphs. In this note, we extend the latter result to the larger family of claw-free cubic multigraphs |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00418 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On 2-bisections and monochromatic edges in claw-free cubic multigraphs Romaniello, Federico Combinatorics A $k$-bisection of a multigraph $G$ is a partition of its vertex set into two parts of the same cardinality such that every component of each part has at most $k$ vertices. Cui and Liu shown that every claw-free cubic multigraph contains a $2$-bisection, while Eom and Ozeki constructed specific $2$-bisections with bounded number of monochromatic edges. Their bound is the best possible for claw-free cubic simple graphs. In this note, we extend the latter result to the larger family of claw-free cubic multigraphs |
| title | On 2-bisections and monochromatic edges in claw-free cubic multigraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.00418 |