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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.00418 |
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Table of 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