On the packing chromatic number of Cartesian products, hexagonal lattice, and trees
Discrete Applied Mathematics
The packing chromatic number of infinite product graphs
European Journal of Combinatorics
Complexity of the packing coloring problem for trees
Discrete Applied Mathematics
| Hi-index | 0.04 |
A packingk-coloring of a graph G is a k-coloring such that the distance between two vertices having color i is at least i+1. To compute the packing chromatic number is NP-hard, even restricted to trees, and it is known to be polynomial time solvable only for a few graph classes, including cographs and split graphs. In this work, we provide upper bounds for the packing chromatic number of lobsters and we prove that it can be computed in polynomial time for an infinite subclass of them, including caterpillars. In addition, we provide superclasses of split graphs where the packing chromatic number can be computed in polynomial time. Moreover, we prove that the packing chromatic number can be computed in polynomial time for the class of partner limited graphs, a superclass of cographs, including also P"4-sparse and P"4-tidy graphs.