Majority C-colorings satisfy mc(P_n^k) = mc(C_n^k) = floor(n/(k+1)), mc(G) + chi(G) <= n+1, non-monotonicity under edge deletion with sharp bounds, and NP-completeness of deciding mc(G) >= k for fixed k >= 2, with a linear-time algorithm for trees.
Sterboul,A new combinatorial parameter
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Majority C-coloring of graphs
Majority C-colorings satisfy mc(P_n^k) = mc(C_n^k) = floor(n/(k+1)), mc(G) + chi(G) <= n+1, non-monotonicity under edge deletion with sharp bounds, and NP-completeness of deciding mc(G) >= k for fixed k >= 2, with a linear-time algorithm for trees.