Some results on Minimum Consistent Subsets of Trees

03/04/2023

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by   Bubai Manna, et al.

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For a graph G = (V,E) where each vertex is coloured by one of k colours, consider a subset C of V such that for each vertex v in V, its set of nearest neighbours in C contains at least one vertex of the same colour as v. Such a C is called a consistent subset (CS). Computing a consistent subset of the minimum size is called the Minimum Consistent Subset problem (MCS). MCS is known to be NP-complete for planar graphs. We propose a polynomial-time algorithm for finding a minimum consistent subset of a k-chromatic spider graph when k is a constant. We also show MCS remains NP-complete on trees.