Circular chromatic index of small graphs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910047095750656 |
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| author | Mazák, Ján Zrubák, Filip |
| author_facet | Mazák, Ján Zrubák, Filip |
| contents | We systematically determine circular chromatic index of small graphs and multigraphs with maximum degree $4$, $5$, $6$ (and also their number for a given small order). We construct several infinite families of such graphs with circular chromatic index in the set $\{Δ+ 1/2, Δ+ 2/3, Δ+ 3/4$, $Δ+ 1\}$. Our results refute edge-connectivity variants of the ``Upper Gap Conjecture'' (about the non-existence of graphs with circular chromatic index just below $Δ+ 1$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08822 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Circular chromatic index of small graphs Mazák, Ján Zrubák, Filip Combinatorics Discrete Mathematics 05C15 We systematically determine circular chromatic index of small graphs and multigraphs with maximum degree $4$, $5$, $6$ (and also their number for a given small order). We construct several infinite families of such graphs with circular chromatic index in the set $\{Δ+ 1/2, Δ+ 2/3, Δ+ 3/4$, $Δ+ 1\}$. Our results refute edge-connectivity variants of the ``Upper Gap Conjecture'' (about the non-existence of graphs with circular chromatic index just below $Δ+ 1$). |
| title | Circular chromatic index of small graphs |
| topic | Combinatorics Discrete Mathematics 05C15 |
| url | https://arxiv.org/abs/2603.08822 |