Fixed-Parameter Tractability of Graph Modification Problems for Hereditary Properties

This paper is concerned with the fixed-parameter tractability of the problem of deciding whether a graph can be made into a graph with a specified hereditary property by deleting at most i vertices, at most j edges, and adding at most k edges, where i, j, k are fixed integers. It is shown that this problem is fixed-parameter tractable whenever the hereditary property can be characterized by a finite set of forbidden induced subgraphs. Furthermore, the problem of deciding whether a graph can be made into a chordal graph by adding a fixed number k of edges is shown to be solvable in 0( 4’( k + 1) --3’2 (m + n) ) time, and is thus fixed-parameter tractable.