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A graph is König-Egerváry if the size of a minimum vertex cover equals that of a maximum matching in the graph. These graphs have been studied extensively from a graph-theoretic point of view. In this paper, we introduce and study the algorithmic complexity of finding König-Egerváry subgraphs of a given graph. In particular, given a graph G and a… (More)

The class of graphs where the size of a minimum vertex cover equals that of a maximum matching is known as König-Egerváry graphs. König-Egerváry graphs have been studied extensively from a graph theoretic point of view. In this paper, we introduce and study the algorithmic complexity of finding maximum König-Egerváry subgraphs of a given graph. More… (More)

A graph is König-Egerváry if the size of a minimum vertex cover equals the size of a maximum matching in the graph. We show that the problem of deleting at most k vertices to make a given graph König-Egerváry is fixed-parameter tractable with respect to k. This is proved using interesting structural theorems on matchings and vertex covers which could be… (More)

We investigate the approximability of minimum and maximum linear ordering problems (MIN-LOP and MAX-LOP) and related feedback set problems such as maximum weight acyclic subdiagraph (MAX-W-SUBDAG), minimum weight feedback arc/vertex set (MIN-W-FAS/ MIN-W-FVS) and a generalization of the latter called MIN-Subset-FAS/MIN-Subset-FVS. MAX-LOP and the other… (More)

In this paper, we investigate the approximability of two node deletion problems. Given a vertex weighted graph G = (V, E) and a specified, or " distinguished " vertex p ∈ V , MDD(min) is the problem of finding a minimum weight vertex set S ⊆ V \ {p} such that p becomes the minimum degree vertex in G[V \ S]; and MDD(max) is the problem of finding a minimum… (More)