Some results on Minimum Consistent Subsets of Trees

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

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum