Spectral Radius, Edge-Disjoint Cycles and Cycles of the Same Length
Huiqiu Lin, Mingqing Zhai, Yanhua Zhao
Abstract
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.
Topics & Concepts
MathematicsDisjoint setsCombinatoricsSpectral radiusGraphEnhanced Data Rates for GSM EvolutionDiscrete mathematicsComputer scienceEigenvalues and eigenvectorsPhysicsQuantum mechanicsTelecommunicationsGraph theory and applicationsLimits and Structures in Graph TheoryAdvanced Graph Theory Research