[gt.go] - "Smaller Universal Graphs for Caterpillars and Graphs of Bounded Path-Width (part 2)" by Cyril Gavoille

/Exposé en français/Talk in french / Transparents en anglais/English slides/

In this talk, I will given a rather simple construction of a graph U n with at most 8n vertices with the property that every n-vertex caterpillar is isomorphic to some induced-subgraph of U n . Previous constructions of so-called induced-universal graph for caterpillars used 256n vertices in the best (Bonichon et al. SIROCCO'06 and Alstrup et al. FOCS'15).

Then, I will also present an extension to path-width-p graphs with an induced-universal graph of n.2 O(p) vertices. This is complemented with a n.2 Ω(p) lower bound. With bounded path-width graphs, our
construction considerably enlarge the family of n-vertex graphs having an induced-universal graph of O(n) vertices, which is optimal. Such unexpected property was known only for trees, bounded maximum degree outerplanar graphs and maximum degree-2 graphs.

The extended result is obtained from an algorithmic approach by designing an adjacency labeling scheme for these graphs using log(n) + O(p) bit vertex labels and with a constant time adjacency test.

This is a joint work with Arnaud Labourel.

[Cyril Gavoille] (Université de Bordeaux )


Remarks / Remarques

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https://webconf.u-bordeaux.fr/b/mar-ef4-zed and LaBRI/178