## Section: New Results

### Linear-time Constant-ratio Approximation Algorithm and Tight Bounds for the Contiguity of Co-graphs

Participant : Christophe Crespelle.

We consider a graph parameter called *contiguity* which aims at encoding a graph by a linear ordering of its vertices. The purpose is to obtain very compact encoding of a graph which still answers in optimal time to neighbourhood queries on the graph (*i.e.* list the neighbours of a given vertex). This allows to deal with very large instances of graphs by loading them entirely into the memory, without penalising the running time of algorithms treating those instances. We designed a linear time algorithm for computing a constant-ratio approximation of the contiguity of an arbitrary co-graph. Our algorithm does not only give an approximation of the parameter, but also provides an encoding of the co-graph realising this value [10]