Spectral radius, edge-disjoint cycles and cycles of the same length

Abstract

In this paper, we give spectral conditions to guarantee the existence of two edge disjoint cycles and two cycles of the same length. These two results can be seen as spectral analogues of Erdős and Posa's size condition and Erdős' classic problem on non existence of two cycles of the same length. By using double leading eigenvectors skill, we further give spectral condition to guarantee the existence of $k$ edge disjoint triangles.

20 pages