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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00135529" target="_blank" >RIV/00216224:14330/24:00135529 - isvavai.cz</a>

Výsledek na webu

<a href="https://arxiv.org/abs/2202.12536" target="_blank" >https://arxiv.org/abs/2202.12536</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.disc.2024.113876" target="_blank" >10.1016/j.disc.2024.113876</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10200 - Computer and information sciences

Projekt

<a href="/cs/project/GA20-04567S" target="_blank" >GA20-04567S: Struktura efektivně řešitelných případů těžkých algoritmických problémů na grafech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

DISCRETE MATHEMATICS

ISSN

0012-365X

e-ISSN

1872-681X

Svazek periodika

347

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

20

Strana od-do

113876

Kód UT WoS článku

001252097100001

EID výsledku v databázi Scopus

2-s2.0-85182798027