Twin-Width and Transductions of Proper k-Mixed-Thin Graphs
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Proceedings |
| Conference | WG 2022: Graph-Theoretic Concepts in Computer Science |
| MU Faculty or unit | |
| Citation | |
| Web | |
| Doi | http://dx.doi.org/10.1007/978-3-031-15914-5_4 |
| Keywords | twin-width;proper interval graph;proper mixed-thin graph;transduction equivalence |
| Description | 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 ??'. |
| Related projects: |