/manager/Index ${session.getAttribute("locale")} 5 Algorithmic aspects of dominator colorings in graphs /manager/Repository/uon:13454 Xd(G). In the DOMINATOR COLORING (DC) problem, a graph G and a positive integer k are given as input and the objective is to check whether Xd(G) ≤ k. We first show that unless P=NP, DC cannot be solved in polynomial time on bipartite, planar, or split graphs. This resolves an open problem posed by Chellali and Maffray [Dominator Colorings in Some Classes of Graphs, Graphs and Combinatorics, 2011] about the polynomial time solvability of DC on chordal graphs. We then complement these hardness results by showing that the problem is fixed parameter tractable (FPT) on chordal graphs and in graphs which exclude a fixed apex graph as a minor.]]> Sat 24 Mar 2018 08:17:07 AEDT ]]> On chromatic transversal domination in graphs /manager/Repository/uon:27527 Sat 24 Mar 2018 07:28:58 AEDT ]]>