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arXiv · 2401.05523

On the Number of Vertices/Edges whose Deletion Preserves the Konig-Egervary Property

Vadim E. Levit·Eugen Mandrescu
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Abstract

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.

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Vadim E. Levit, Eugen Mandrescu. 2024-01-10. On the Number of Vertices/Edges whose Deletion Preserves the Konig-Egervary Property. https://arxiv.org/abs/2401.05523

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