1. Cycle separating cuts in possible counterexamples to the cycle double cover and the Berge-Fulkerson conjecturesEdita Máčajová, Giuseppe Mazzuoccolo, Gloria Tabarelli, 2026, izvirni znanstveni članek Opis: 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.
Ključne besede: snark, cyclic connectivity, cycle double cover, Berge-Fulkerson conjecture
Objavljeno v RUP: 03.03.2026; Ogledov: 1449; Prenosov: 77
 Celotno besedilo (412,02 KB) |
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3. Algebraic aspects of graph theory : PhD thesisAdemir Hujdurović, 2013, doktorska disertacija Ključne besede: circulant, bicirculant, semiregular automorphism, vertex-transitive graph, half-arc-transitive graph, snark, Cayley graph, quasi m-Cayley graph, generalized Cayley graph, I-regular action, regular cover of a graph, automorphism group
Objavljeno v RUP: 10.07.2015; Ogledov: 7406; Prenosov: 71
Celotno besedilo (5,38 MB) |
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