Twin-Width and Transductions of Proper k-Mixed-Thin Graphs
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Periodical |
| Magazine / Source | DISCRETE MATHEMATICS |
| MU Faculty or unit | |
| Citation | |
| web | https://arxiv.org/abs/2202.12536 |
| Doi | http://dx.doi.org/10.1016/j.disc.2024.113876 |
| Keywords | twin-width;proper interval graph;proper mixed-thin graph;transduction equivalence |
| Description | The new graph parameter twin-width, introduced by Bonnet, Kim, Thomassé and Watrigant in 2020, 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, classes of efficiently bounded 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 slight subclass of k-mixed-thin graphs is transduction-equivalent to posets of width such that there is a quadratic-polynomial relation between k and . In addition to that, we also give an abstract overview of the so-called red potential method which we use to prove our twin-width bounds. |
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