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Cographs are those graphs without induced path on four vertices. A graph G is a probe cograph if its vertex set can be partitioned into two sets, N (non-probes) and P (probes) where N is independent and G can be extended to a cograph by adding edges between certain non-probes. A partitioned probe cograph is a probe cograph with a given partition in N and P.(More)
Modular decomposition of graphs is a powerful tool for designing efficient algorithms for problems on graphs such as Maximum Weight Stable Set (MWS) and Maximum Weight Clique. Using this tool we obtain O(n·m) time algorithms for MWS on chair-and xbull-free graphs which considerably extends an earlier result on bull-and chair-free graphs by De Simone and(More)
Graph class C is induced-hereditary if for every graph G in C, every induced subgraph of G belongs to C. Induced-hereditary graph classes allow characterisation by sets of forbidden induced subgraphs. Such characterisations are very useful for automatic deduction of relations between graph classes. However, sometimes those sets of forbidden induced(More)
A graph class is called A-free if every graph in the class has no graph in the set A as an induced subgraph. Such characterisations by forbidden induced subgraphs are (among other purposes) very useful for determining whether A-free is a subclass of B-free, by determining whether every graph in B has some graph in A as an induced subgraph. This requires(More)