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

Varování

Publikace nespadá pod Ekonomicko-správní fakultu, ale pod Fakultu informatiky. Oficiální stránka publikace je na webu muni.cz.

Autoři	BALABÁN Jakub HLINĚNÝ Petr JEDELSKÝ Jan
Rok publikování	2022
Druh	Článek ve sborníku
Konference	WG 2022: Graph-Theoretic Concepts in Computer Science
Fakulta / Pracoviště MU	Fakulta informatiky
Citace
www	https://arxiv.org/abs/2202.12536 https://link.springer.com/chapter/10.1007/978-3-031-15914-5_4
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 ??'.
Související projekty:	Structure of tractable instances of hard algorithmic problems on graphs Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity 22 Rozsáhlé výpočetní systémy: modely, aplikace a verifikace XI.