On $4$-covers of cubic graphs with two adjacent odd circuits in a $2$-factor
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910206005346304 |
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| author | Karabáš, Ján Máčajová, Edita |
| author_facet | Karabáš, Ján Máčajová, Edita |
| contents | Let $G$ be a cubic graph admitting a $2$-factor consisting of exactly two odd circuits, and let the complementary $1$-factor contain precisely three spokes (along with an arbitrary number of chords). We show that four perfect matchings can cover $G$. As a consequence, $G$ fulfils the 7/5-Conjecture of Alon and Tarsi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09475 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On $4$-covers of cubic graphs with two adjacent odd circuits in a $2$-factor Karabáš, Ján Máčajová, Edita Combinatorics 05C15, 05C70, 05C75 Let $G$ be a cubic graph admitting a $2$-factor consisting of exactly two odd circuits, and let the complementary $1$-factor contain precisely three spokes (along with an arbitrary number of chords). We show that four perfect matchings can cover $G$. As a consequence, $G$ fulfils the 7/5-Conjecture of Alon and Tarsi. |
| title | On $4$-covers of cubic graphs with two adjacent odd circuits in a $2$-factor |
| topic | Combinatorics 05C15, 05C70, 05C75 |
| url | https://arxiv.org/abs/2605.09475 |