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Twin-width and Transductions of Proper k-Mixed-Thin Graphs
- Publication Year :
- 2022
-
Abstract
- The new graph parameter twin-width, introduced by Bonnet, Kim, Thomass e 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 k' such that there is a quadratic-polynomial relation between k and k'. 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.
- Subjects :
- Mathematics - Combinatorics
Computer Science - Discrete Mathematics
68R10, 05C62
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2202.12536
- Document Type :
- Working Paper