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

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• 作者：Jonas H?gglund ; Klas Markstr?m
• 关键词：Stable cycle ; Snark ; Cycle double cover ; Semiextension
• 刊名：Discrete Mathematics
• 出版年：2012
• 出版时间：6 September, 2012
• 年：2012
• 卷：312
• 期：17
• 页码：2540-2544
• 全文大小：448 K

文摘

A cycle in a graph is called stable if there exists no other cycle in the same graph such that . In this paper, we study stable cycles in snarks and we show that if a cubic graph has a cycle of length at least 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.