图的λ_4-最优性的邻域交条件

Neighborhood Intersection Conditions for λ_4-Optimality in Graphs

文章给出了图的λ4-最优性的邻域交条件.设图G是阶至少为34的λ4-连通图,若对G中任意一对不相邻顶点u,v,都有|N(u)∩N(v)|≥6且ξ4(G)≤3n(G)/2+3,则G是λ4-最优的;若对于λ4-连通图G中任意一对不相邻顶点u,v,都有|N(u)∩N(v)|≥6且对图中每个三角形T至少存在一个顶点v∈V(T)使得d(v)≥n(G)/2+3,则G是λ4-最优的.

We will see two neighborhood intersection conditions for λ4-optimality in graphs.Let G be a λ4-connected graph with ｜V（G）｜≥34.If ｜N（u）∩N（v）｜≥6 for all pairs u,v of nonadjacent vertices and ξ4（G）≤3n（G）/2＋3,then G is λ4-optimal.Let G be a λ4-connected graph satisfying ｜N（u）∩N（v）｜≥6 for all pair u,v of nonadjacent vertices.If for each triangle T there exists at least one vertex v∈V（T） making d（v）≥n（G）/2＋3,then G is λ4-optimal.