Spectral Radius, Edge-Disjoint Cycles and Cycles of the Same Length
Copyright policy )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 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.
- Chuzhou University China (People's Republic of)
- East China University of Science and Technology China (People's Republic of)
- North China University of Science and Technology China (People's Republic of)
Extremal problems in graph theory, Distance in graphs, Graphs and linear algebra (matrices, eigenvalues, etc.), G.2, edge-disjoint cycles, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), spectral radius of a graph, Paths and cycles, 05C50, 05C35
Extremal problems in graph theory, Distance in graphs, Graphs and linear algebra (matrices, eigenvalues, etc.), G.2, edge-disjoint cycles, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), spectral radius of a graph, Paths and cycles, 05C50, 05C35
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