Twin-Width and Transductions of Proper k-Mixed-Thin Graphs
| Autoři | |
|---|---|
| Rok publikování | 2022 |
| Druh | Článek ve sborníku |
| Konference | WG 2022: Graph-Theoretic Concepts in Computer Science |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | |
| Doi | http://dx.doi.org/10.1007/978-3-031-15914-5_4 |
| Klíčová slova | twin-width;proper interval graph;proper mixed-thin graph;transduction equivalence |
| Popis | The new graph parameter twin-width, recently introduced by Bonnet et al., allows for an FPT algorithm for testing all FO properties of graphs. This makes classes of efficiently bounded twin-width attractive from the algorithmic point of view. In particular, such classes (of small twin-width) include proper interval graphs, and (as digraphs) posets of width k. Inspired by an existing generalization of interval graphs into so-called k-thin graphs, we define a new class of proper k-mixed-thin graphs which largely generalizes proper interval graphs. We prove that proper k-mixed-thin graphs have twin-width linear in k, and that a certain subclass of k-mixed-thin graphs is transduction-equivalent to posets of width ??' such that there is a quadratic relation between k and ??'. |
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