The graph G=(V,E) is called Konig-Egervary if the sum of its independence number and its matching number equals its order. Let RV(G) denote the number of vertices v such that G-v is Konig-Egervary, and let RE(G) denote the number of edges e such that G-e is Konig-Egervary. Clearly, RV(G) = |V| and RE(G) = |E| for bipartite graphs. Unlike the bipartiteness, the property of being a Konig-Egervary graph is not hereditary. In this paper, we present an equality expressing RV(G) in terms of some graph parameters, and a tight inequality bounding RE(G) in terms of the same parameters, when G is Konig-Egervary.

翻译：若图G=(V,E)的独立数与其匹配数之和等于其顶点数，则称其为König-Egervary图。令RV(G)表示满足G-v为König-Egervary图的顶点v的数量，RE(G)表示满足G-e为König-Egervary图的边e的数量。显然，对于二分图有RV(G)=|V|且RE(G)=|E|。与二分性不同，König-Egervary图的性质不具备遗传性。本文提出一个等式，用若干图参数表示König-Egervary图G的RV(G)；同时给出一个紧致不等式，用相同参数对RE(G)进行界定。