Spectral condition for the existence of a chorded cycle

2023/11/22 by Zheng, Jiaxin, Huang, Xueyi, Wang, Junjie
#05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.13323

Abstract

A chord of a cycle C is an edge joining two non-consecutive vertices of C. A cycle C in a graph G is chorded if the vertex set of C induces at least one chord. In this paper, we prove that if G is a graph with order n≥ 6 and ρ(G)≥ ρ(K_2,n-2), then G contains a chorded cycle unless G≅ K_2,n-2. This gives one answer to a question posed by Gould [Results and problems on chorded cycles: A survey, Graphs Combin. 38 (2022) 189].

Related

• Spectral conditions implying the existence of doubly chorded cycles without or with constraints
• Spectral conditions for the existence of chorded cycles in graphs with fixed size
• Answers to Gould's question concerning the existence of chorded cycles
• Disjoint chorded cycles in a 2-connected graph
• Partitioning a graph into cycles with a specified number of chords