Work

Cycle separating cuts in possible counterexamples to the cycle double cover and the Berge-Fulkerson conjectures

Year: 2025

Type: article

Abstract: It is known that smallest counterexamples to 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 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 219 a priori possibilities. Similarly, for the Berge-Fulkerson Conjecture, we prove that among more than 2111 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.

Source: Ars Mathematica Contemporanea

DOI: 10.26493/1855-3974.3409.c13

Authors: Edita Máčajová, Giuseppe Mazzuoccolo, Gloria Tabarelli

Institutions: Comenius University Bratislava, University of Modena and Reggio Emilia, University of Verona

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408302117

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