2015/12/08 by Saieed Akbari, Khashayar Etemadi, Akbari, Saieed +5
Computer Science · Engineering · #Advanced Graph Theory Research #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Interconnection Networks and Systems #cs.DM #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1512.02443
arxiv created 2015/12/08 · openalex publication_date 2015/12/08 · arxiv updated 2015/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we provide some sufficient conditions for the existence of an odd or even cycle that passing a given vertex or an edge in 2-connected or 2-edge connected graphs. We provide some similar conditions for the existence of an odd or even circuit that passing a given vertex or an edge in 2-edge connected graphs. We show that if G is a 2-connected k-regular graph, k ≥ 3, then every edge of G is contained in an even cycle. We also prove that in a 2-edge connected graph, if a vertex has odd degree, then there is an even cycle containing this vertex.