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arXiv · 2303.02337

Some results on Minimum Consistent Subsets of Trees

Bubai Manna·Bodhayan Roy
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Abstract

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\C, 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.

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Bubai Manna, Bodhayan Roy. 2023-03-04. Some results on Minimum Consistent Subsets of Trees. https://arxiv.org/abs/2303.02337

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