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Article Dans Une Revue Discrete Mathematics Année : 2016

Linearity is Strictly More Powerful than Contiguity for Encoding Graphs

Résumé

Linearity and contiguity are two parameters devoted to graph encoding. Linearity is a generalization of contiguity in the sense that every encoding achieving contiguity k induces an encoding achieving linearity k, both encoding having size Theta(k.n), where n is the number of vertices of G. In this paper, we prove that linearity is a strictly more powerful encoding than contiguity, i.e. there exists some graph family such that the linearity is asymptotically negligible in front of the contiguity. We prove this by answering an open question asking for the worst case linearity of a cograph on n vertices: we provide an O(log n/log log n) upper bound which matches the previously known lower bound

Dates et versions

hal-01424428 , version 1 (02-01-2017)

Identifiants

Citer

Christophe Crespelle, Tien-Nam Le, Kévin Perrot, Thi Ha Duong Phan. Linearity is Strictly More Powerful than Contiguity for Encoding Graphs. Discrete Mathematics, 2016, 339 (8), pp.2168-2177. ⟨10.1016/j.disc.2016.03.006⟩. ⟨hal-01424428⟩
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