| Title: | Cycle separating cuts in possible counterexamples to the cycle double cover and the Berge-Fulkerson conjectures |
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| Authors: | ID Máčajová, Edita (Author)
ID Mazzuoccolo, Giuseppe (Author)
ID Tabarelli, Gloria (Author) |
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| Files: |  AMC_Macajova,_Mazzuoccolo,_Tabarelli_2026.pdf (412,02 KB)
MD5: 34FAE9D96BE480EAD5E1A908F013C98C
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | It is known that smallest counterexamples to the Cycle Double Cover Conjecture and Berge-Fulkerson Conjecture (if they exist) are cyclically 4- and 5-edge-connected, respectively. We further analyse small cycle separating cuts in possible counterexamples. We prove that if a smallest counterexample G to the CDC Conjecture contains a cycle separating 4-cut S, then the behaviour of the admissible CDC coverings along the dangling edges of the two 4-poles induced by S is uniquely determined among more than 2 a priori possibilities. Similarly, for the Berge-Fulkerson Conjecture, we prove that among more than 2 a priori possibilities, there are only 13 pairs of admissible sets that could occur along the dangling edges of a 5-cut in a smallest counterexample. |
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| Keywords: | snark, cyclic connectivity, cycle double cover, Berge-Fulkerson conjecture |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 21.01.2026 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 22 str. |
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| Numbering: | Vol. 26, no. 2, [article no.] P2.03 |
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| PID: | 20.500.12556/RUP-22692  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3409.c13 |
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| Publication date in RUP: | 03.03.2026 |
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| Views: | 77 |
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| Downloads: | 2 |
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