Sparse Graphs of Twin-width 2 Have Bounded Tree-width

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F23%3A00131580" target="_blank" >RIV/00216224:14330/23:00131580 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4230/LIPICS.ISAAC.2023.11" target="_blank" >http://dx.doi.org/10.4230/LIPICS.ISAAC.2023.11</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPICS.ISAAC.2023.11" target="_blank" >10.4230/LIPICS.ISAAC.2023.11</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Sparse Graphs of Twin-width 2 Have Bounded Tree-width

Popis výsledku v původním jazyce

Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS 2020]. Very briefly, its essence is a gradual reduction (a contraction sequence) of the given graph down to a single vertex while maintaining limited difference of neighbourhoods of the vertices, and it can be seen as widely generalizing several other traditional structural parameters. Having such a sequence at hand allows to solve many otherwise hard problems efficiently. Our paper focuses on a comparison of twin-width to the more traditional tree-width on sparse graphs. Namely, we prove that if a graph G of twin-width at most 2 contains no K_{t,t} subgraph for some integer t, then the tree-width of G is bounded by a polynomial function of t. As a consequence, for any sparse graph class C we obtain a polynomial time algorithm which for any input graph G ∈ C either outputs a contraction sequence of width at most c (where c depends only on C), or correctly outputs that G has twin-width more than 2. On the other hand, we present an easy example of a graph class of twin-width 3 with unbounded tree-width, showing that our result cannot be extended to higher values of twin-width.

Název v anglickém jazyce

Sparse Graphs of Twin-width 2 Have Bounded Tree-width

Popis výsledku anglicky

Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS 2020]. Very briefly, its essence is a gradual reduction (a contraction sequence) of the given graph down to a single vertex while maintaining limited difference of neighbourhoods of the vertices, and it can be seen as widely generalizing several other traditional structural parameters. Having such a sequence at hand allows to solve many otherwise hard problems efficiently. Our paper focuses on a comparison of twin-width to the more traditional tree-width on sparse graphs. Namely, we prove that if a graph G of twin-width at most 2 contains no K_{t,t} subgraph for some integer t, then the tree-width of G is bounded by a polynomial function of t. As a consequence, for any sparse graph class C we obtain a polynomial time algorithm which for any input graph G ∈ C either outputs a contraction sequence of width at most c (where c depends only on C), or correctly outputs that G has twin-width more than 2. On the other hand, we present an easy example of a graph class of twin-width 3 with unbounded tree-width, showing that our result cannot be extended to higher values of twin-width.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

ISAAC 2023

ISBN

9783959772891

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

13

Strana od-do

„11:1“-„11:13“

Název nakladatele

Schloss Dagstuhl -- Leibniz-Zentrum f{"u}r Informatik

Místo vydání

Dagstuhl, Germany

Místo konání akce

Kyoto, Japan

Datum konání akce

1. 1. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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