论文标题
光谱半径和彩虹匹配
Spectral radius and rainbow matchings of graphs
论文作者
论文摘要
令$ n，m $为整数，以便$ 1 \ leq m \ leq（n-2）/2 $，让$ [n] = \ {1，\ ldots，n \} $。令$ \ Mathcal {g} = \ {g_1，\ ldots，g_ {m+1} \} $是同一顶点集合$ [n] $的图形家族。在本文中，我们证明，如果对于[m+1] $中的任何$ i \，$ g_i $的光谱半径不少于$ \ max \ {2m，\ frac {1} {2} {2} {2} {m-1+\ sqrt {（m-1）即，除非$ g_1 = g_1 = g_2 = \ ldots = g_ {m+1} $和$ g_1 \ in \ in \ {2m+1} \ cup（n-2m-1）k_1，k_1，k_m \ vee（k_m \ vee（n-m-m）k_1
Let $n,m$ be integers such that $1\leq m\leq (n-2)/2$ and let $[n]=\{1,\ldots,n\}$. Let $\mathcal{G}=\{G_1,\ldots,G_{m+1}\}$ be a family of graphs on the same vertex set $[n]$. In this paper, we prove that if for any $i\in [m+1]$, the spectral radius of $G_i$ is not less than $\max\{2m,\frac{1}{2}(m-1+\sqrt{(m-1)^2+4m(n-m)})\}$, then $\mathcal{G}$ admits a rainbow matching, i.e. a choice of disjoint edges $e_i\in G_i$, unless $G_1=G_2=\ldots=G_{m+1}$ and $G_1\in \{K_{2m+1}\cup (n-2m-1)K_1, K_m\vee (n-m)K_1\}$.
