Abstract
Linearity and contiguity are two parameters devoted to graph encoding. Linearity is a generalisation 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.
This work was partially funded by a grant from Région Rhône-Alpes and by the delegation program of CNRS.
This work was partially funded by the Vietnam Institute for Advanced Study in Mathematics (VIASM) and by the Vietnam National Fondation for Science and Technology Developement (NAFOSTED).
This work was partially funded by Fondecyt Postdoctoral grant 3140527 and Núcleo Milenio Información y Coordinación en Redes (ACGO).
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Crespelle, C., Le, TN., Perrot, K., Phan, T.H.D. (2015). Linearity Is Strictly More Powerful Than Contiguity for Encoding Graphs. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_18
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DOI: https://doi.org/10.1007/978-3-319-21840-3_18
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