Twin-Width and Transductions of Proper k-Mixed-Thin Graphs

BALABÁN, Jakub, Petr HLINĚNÝ and Jan JEDELSKÝ. Twin-Width and Transductions of Proper k-Mixed-Thin Graphs. DISCRETE MATHEMATICS. NETHERLANDS: ELSEVIER, 2024, p. to appear, 20 pp. ISSN 0012-365X. Available from: https://dx.doi.org/10.1016/j.disc.2024.113876.

Basic information

• Original name: Twin-Width and Transductions of Proper k-Mixed-Thin Graphs
• Authors: BALABÁN, Jakub, Petr HLINĚNÝ and Jan JEDELSKÝ.
• Edition: DISCRETE MATHEMATICS, NETHERLANDS, ELSEVIER, 2024, 0012-365X.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10200 1.2 Computer and information sciences
• Country of publisher: Netherlands
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.800 in 2022
• Organization unit: Faculty of Informatics
• Doi: http://dx.doi.org/10.1016/j.disc.2024.113876
• Keywords in English: twin-width;proper interval graph;proper mixed-thin graph;transduction equivalence
• Tags: International impact, Reviewed

Abstract

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.