Titre : Finite obstructions to graph partitions

Exposant : Pavol Hell, Simon Fraser University

Consider graph partitions with possible restrictions on the parts, and on the connections between parts: the restrictions can be that there are no edges, or that all possible edges are present. Many partitions arising in the study of perfect graphs have this flavour. In some cases the existence of such a partition is characterized by the absence of finitely many forbidden induced subgraphs. We ask when this is the case, and give some general answers, and some answers for special graph classes, such as chordal graphs. These include joint results with T. Feder, S. Nekooei Rizi, W. Xie, O. Shklarsky, and others. For those who will have attended my talk at LIAFA, I will add some new topics.