λ_4-最优二部图的领域交条件

Neighborhood Intersection Conditions for λ_4-Optimality in Bipartite Graphs

文章给出了二部图是λ4-最优的一个领域交条件.设n为一个不小于8的正整数,令G=(X∪Y,E)为一个n阶二部图且ξ4(G)≤n/2.若G有一个饱和X或Y中所有顶点的匹配且对任意的u,v∈X和u,v∈Y都有|N(u)∩N(v)|≥4,则G是λ4-最优的.

We mainly study the neighborhood intersection conditions for λ_4-optimality inbipartite graphs. Let n≥8 be an integer and let G=（XUY,E） be a bipartite graph of order n and n 4（G）≤n/2, If G has a matching that saturates every vertex in X or every vertex in Y and [N（u） [/ N（v） ]≥4 for any u,v∈Y or u,v∈X,then G is λ_4- optimal.