A C-coloured graph is a graph, that is possibly directed, where the edges are coloured with colours from the set C. Clique-width is a complexity measure for C-coloured graphs, for finite sets C.… (More)

We show how to use the split decomposition to solve some NP-hard optimization problems on graphs. We give algorithms for clique problem and domination-type problems. Our main result is an algorithm… (More)

Every binary word with at least four letters contains a square. A. Fraenkel and J. Simpson showed that three distinct squares are necessary and sufficient to construct an infinite binary word. We… (More)

We prove that 2-abelian-cubes are avoidable over a binary alphabet and that 3-abelian-squares are avoidable over a ternary alphabet, answering positively to two questions of Karhumäki et al.. We also… (More)

We study the avoidability of long k-abelian-squares and k-abeliancubes on binary and ternary alphabets. For k = 1, these are Mäkelä’s questions. We show that one cannot avoid abelian-cubes of abelian… (More)