Minimum Consistent Subset for Trees Revisited

05/12/2023

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by   Hiroki Arimura, et al.

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In a vertex-colored graph G = (V, E), a subset S ⊆ V is said to be consistent if every vertex has a nearest neighbor in S with the same color. The problem of computing a minimum cardinality consistent subset of a graph is known to be NP-hard. On the positive side, Dey et al. (FCT 2021) show that this problem is solvable in polynomial time when input graphs are restricted to bi-colored trees. In this paper, we give a polynomial-time algorithm for this problem on k-colored trees with fixed k.