Stable dominating circuits in snarks
نویسندگان
چکیده
منابع مشابه
Dominating Circuits in Regular Matroids
In 1971, Nash-Williams proved that if G is a simple 2-connected graph on n vertices having minimum degree at least 3 (n+ 2), then any longest cycle C in G is also edge-domininating; that is, each edge of G has at least one end-vertex incident with a vertex of C. We say that a circuit C in a matroid M is dominating if each component of M/C has rank at most one. In this paper, we show that an ana...
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An eulerian subgraph of a graph is called a circuit. As shown by Harary and Nash-Williams, the existence of a Hamilton cycle in the line graph L(G) of a graph G is equivalent to the existence of a dominating circuit in G, i.e., a circuit such that every edge of G is incident with a vertex of the circuit. Important progress in the study of the existence of spanning and dominating circuits was ma...
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We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is hamiltonian), by Thomassen (every 4-connected line graph is hamiltonian) and by Fleischner (every cyclically 4-edge-connected cubic graph has either a 3-edgecoloring or a dominating cycle), which are known to be equivalent, are equivalent with the statement that every snark (i.e. a cyclically 4-edge-connec...
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In this talk we present snarks whose edges cannot be covered by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family of such snarks, generalising an example provided by Hägglund. We construct another infinite family, arising from a generalisation in a different direction. The proof that this family has the requested property is computer-assisted. In addition, we p...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2001
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00244-2