Abstract
Let n,m be integers such that 1≤m≤(n−2)/2 and let [n]={1,…,n}. Let G={G1,…,Gm+1} be a family of graphs on the same vertex set [n]. In this paper, we prove that if for any i∈[m+1], the spectral radius of Gi is not less than max{2m,12(m−1+(m−1)2+4m(n−m))}, then G admits a rainbow matching, i.e. a choice of disjoint edges ei∈Gi, unless G1=G2=…=Gm+1 and G1∈{K2m+1∪(n−2m−1)K1,Km∨(n−m)K1}.
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