The spanning k-trees, perfect matchings and spectral radius of graphs

By Dandan Fan, S. Goryainov, Xueyi Huang, Huiqiu Lin. Linear and multilinear algebra, 2021

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A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we provide a sufficient condition for the existence of a k-tree in a connected graph with fixed order in terms of the adjacency spectral radius and the signless Laplacian spectral radius, respectively. Also, we give a similar condition for the existence of a perfect matching in a balanced bipartite graph with fixed order and minimum degree.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/985b2bb8e534375bb050827bdb7ddd0c802e932f