A one-to-one correspondence between potential solutions of the cluster deletion problem and the minimum sum coloring problem, and its application to P4 -sparse graphs
Résumé
In this note we show a one-to-one correspondence between potentially optimal solutions to the cluster deletion problem in a graph G and potentially optimal solutions for the minimum sum coloring problem in G (i.e. the complement graph of G). We apply this correspondence to polynomially solve the cluster deletion problem in a subclass of P 4 -sparse graphs that strictly includes P 4 -reducible graphs.
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