Abstract:We consider a natural combinatorial optimization problem on chordal graphs, the class of graphs with no induced cycle of length four or more. A subset of vertices of a chordal graph is (monophonically) convex if it contains the vertices of all chordless paths between any two vertices of the set. The problem is to find a maximum-weight convex subset of a given vertex-weighted chordal graph. It generalizes previously studied special cases in trees and split graphs. It also happens to be closely related to the cl… Show more
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