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Two edges are called P 4-adjacent if they belong to the same P 4 (chordless path on 4 vertices). P 4-components, in our terminology, are the equivalence classes of the transitive closure of the P 4-adjacency relation. In this paper, new results on the structure of P 4-components are obtained. On the one hand, these results allow us to improve the complexity… (More)

The recognition of threshold graphs, those graphs with threshold dimension one, is well understood and some linear time algorithms are known for this problem. On the other hand, YANNAKAKIS proved that determining if the threshold dimension of a graph is less than or equal to k is NP-complete for all fixed k ~ 3. CHV~TAL and HAMMER conjectured that the… (More)

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