Two-colouring all two-element maximal antichains
Journal of Combinatorial Theory Series A
Discrete Mathematics
On the complexity of bicoloring clique hypergraphs of graphs
Journal of Algorithms
Coloring the Maximal Cliques of Graphs
SIAM Journal on Discrete Mathematics
Clique-coloring some classes of odd-hole-free graphs
Journal of Graph Theory
Clique-Colouring and biclique-colouring unichord-free graphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Clique-transversal sets and clique-coloring in planar graphs
European Journal of Combinatorics
| Hi-index | 5.23 |
A k-clique-coloring of a graph G is an assignment of k colors to the vertices of G such that every maximal (i.e., not extendable) clique of G contains two vertices with different colors. We show that deciding whether a graph has a k-clique-coloring is @S"2^p-complete for every k=2. The complexity of two related problems are also considered. A graph is k-clique-choosable, if for every k-list-assignment on the vertices, there is a clique coloring where each vertex receives a color from its list. This problem turns out to be @P"3^p-complete for every k=2. A graph G is hereditary k-clique-colorable if every induced subgraph of G is k-clique-colorable. We prove that deciding hereditary k-clique-colorability is also @P"3^p-complete for every k=3. Therefore, for all the problems considered in the paper, the obvious upper bound on the complexity turns out to be the exact class where the problem belongs.