Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647000 | Discrete Mathematics | 2016 | 10 Pages |
Abstract
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 Î(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(logn/loglogn) upper bound which matches the previously known lower bound.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Christophe Crespelle, Tien-Nam Le, Kevin Perrot, Thi Ha Duong Phan,