COMPLETE CHARACTERIZATION OF ODD FACTORS VIA THE SIZE, SPECTRAL RADIUS OR DISTANCE SPECTRAL RADIUS OF GRAPHS

摘要

Given a graph G, a {1, 3, ..., 2n - 1}-factor of G is a spanning subgraph of G, in which each degree of vertices is one of {1, 3, ..., 2n - 1} where n is a positive integer. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {1, 3, ..., 2n - 1}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {1, 3, ..., 2n - 1}-factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible.

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