Spectral Radius, Edge-Disjoint Cycles and Cycles of the Same Length

 In this paper, we provide spectral conditions for the existence of two edge-disjoint cycles and two cycles of the same length in a graph, which can be viewed as the spectral analogues of Erdős and Posa's condition and Erdős' classic problem about the maximum number of edges of a graph wit...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 29; no. 2
Main Authors Lin, Huiqiu, Zhai, Mingqing, Zhao, Yanhua
Format Journal Article
LanguageEnglish
Published 08.04.2022
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Summary: In this paper, we provide spectral conditions for the existence of two edge-disjoint cycles and two cycles of the same length in a graph, which can be viewed as the spectral analogues of Erdős and Posa's condition and Erdős' classic problem about the maximum number of edges of a graph without two edge-disjoint cycles and two cycles of the same length, respectively. Furthermore, we give a spectral condition to guarantee the existence of $k$ edge-disjoint triangles in a graph.
ISSN:1077-8926
1077-8926
DOI:10.37236/10783