JAMC
The Signless Laplacian Spectral Radius and Rainbow Matchings (Hamilton Paths) of Graphs
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Abstract
Let and be integers satisfying 1≤m≤(n-2)/2, and let [n]={1,...,n}. Let 
be a family of graphs (not necessarily distinct) defined on the common vertex set 
. A graph H on V is said to be rainbow if there exists a bijection 
such that every edge 
satisfies 
In this paper, we prove that if the signless Laplacian radius 
satisfies the inequality
For each 
, then 
contains a rainbow matching, except when all graphs in are identical and isomorphic to either 
or 
. Furthermore, for 
and 
, we show that if
for each 
, then 
admits a rainbow Hamilton path, unless all graphs in 
are identical and isomorphic to 
.
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How to cite this paper
The Signless Laplacian Spectral Radius and Rainbow Matchings (Hamilton Paths) of Graphs
How to cite this paper: Xiaolong Wang, Haixiang Lv. (2025) The Signless Laplacian Spectral Radius and Rainbow Matchings (Hamilton Paths) of Graphs. Journal of Applied Mathematics and Computation, 9(1), 66-74.
DOI: http://dx.doi.org/10.26855/jamc.2025.03.009
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