Independence and domination in Polygon Graphs

Abstract Given an integer k, k≥3, we define the class of k-polygon graphs to be the intersection graphs of straight-line chords inside a convex k-gon. Thus, permutation graphs form a proper subset of any such class. Moreover, circle graphs = ∪∞k=3 k-polygon graphs. In this paper, we show polynomial time exact algorithms for solving the maximum r-independent set problem (finding a maximum subset of vertices that can be partitioned into r independent sets) and the minimum dominating set problem on k-polygen graphs, for any fixed k.

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