We study vertex colorings of the square G2 of an outerplanar graph G. We find the optimal bound of the inductiveness, chromatic number and the clique number of G2 as a function of...
We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP...
Michal Malafiejski, Krzysztof Giaro, Robert Jancze...
We consider the problem of testing 3-colorability in the bounded-degree model. We show that, for small enough ε, every tester for 3colorability must have query complexity Ω(n)....
We consider the problem of coloring a planar graph with the minimum number of colors so that each color class avoids one or more forbidden graphs as subgraphs. We perform a detail...
Hajo Broersma, Fedor V. Fomin, Jan Kratochví...
We give a graph decomposition technique that creates entirely independent subproblems for graph problems such as coloring and dominating sets that can be solved without synchroniz...