A note on transformations of edge colorings of chordless graphs and triangle-free graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917851874459648 |
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| author | Asratian, Armen |
| author_facet | Asratian, Armen |
| contents | Bonamy et al. (2023) proved that an optimal edge coloring of a simple triangle--free graph $G$ can be reached from any given proper edge coloring of $G$ through a series of Kempe changes. We show that a small modification of their proof gives a possibility to obtain a similar result for a larger class of simple graphs consisting of all triangle-free and all chordless graphs (a graph $G$ is chordless if in every cycle $C$ of $G$ any two nonconsecutive vertices of $C$ are not adjacent). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_19569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on transformations of edge colorings of chordless graphs and triangle-free graphs Asratian, Armen Combinatorics 05C15 G.2.2 Bonamy et al. (2023) proved that an optimal edge coloring of a simple triangle--free graph $G$ can be reached from any given proper edge coloring of $G$ through a series of Kempe changes. We show that a small modification of their proof gives a possibility to obtain a similar result for a larger class of simple graphs consisting of all triangle-free and all chordless graphs (a graph $G$ is chordless if in every cycle $C$ of $G$ any two nonconsecutive vertices of $C$ are not adjacent). |
| title | A note on transformations of edge colorings of chordless graphs and triangle-free graphs |
| topic | Combinatorics 05C15 G.2.2 |
| url | https://arxiv.org/abs/2411.19569 |