Regular colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912263942701056 |
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| author | Karabáš, Ján Máčajová, Edita Nedela, Roman Škoviera, Martin |
| author_facet | Karabáš, Ján Máčajová, Edita Nedela, Roman Škoviera, Martin |
| contents | We introduce a new invariant of a cubic graph - its regular colouring defect - which is defined as the smallest number of edges left uncovered by any collection of three perfect matchings that have no edge in common. This invariant is a modification of colouring defect, an invariant introduced by Steffen (J. Graph Theory 78(2015), 195--206), whose definition does not require the empty intersection condition. In this paper we discuss the relationship of this invariant to the well-known conjectures of Fulkerson (1971) and Fan and Raspaud (1994) and prove that colouring defect and regular colouring defect can be arbitrarily far apart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regular colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson Karabáš, Ján Máčajová, Edita Nedela, Roman Škoviera, Martin Combinatorics 05C15, 05C70 We introduce a new invariant of a cubic graph - its regular colouring defect - which is defined as the smallest number of edges left uncovered by any collection of three perfect matchings that have no edge in common. This invariant is a modification of colouring defect, an invariant introduced by Steffen (J. Graph Theory 78(2015), 195--206), whose definition does not require the empty intersection condition. In this paper we discuss the relationship of this invariant to the well-known conjectures of Fulkerson (1971) and Fan and Raspaud (1994) and prove that colouring defect and regular colouring defect can be arbitrarily far apart. |
| title | Regular colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson |
| topic | Combinatorics 05C15, 05C70 |
| url | https://arxiv.org/abs/2312.13638 |