On stable cycles and cycle double covers of graphs with large circumference

摘要

A cycle C in a graph is called stable if there exists no other cycle D in the same graph such that V(C)?V(D). In this paper, we study stable cycles in snarks and we show that if a cubic graph G has a cycle of length at least |V(G)|-9 then it has a cycle double cover. We also give a construction for an infinite snark family with stable cycles of constant length and answer a question by Kochol by giving examples of cyclically 5-edge connected snarks with stable cycles.