Twin-width of graphs on surfaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00137364" target="_blank" >RIV/00216224:14330/24:00137364 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Twin-width of graphs on surfaces

Popis výsledku v původním jazyce

Twin-width is a width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS'20, JACM'22], which has many structural and algorithmic applications. Hliněný and Jedelský [ICALP'23] showed that every planar graph has twin-width at most 8. We prove that the twin-width of every graph embeddable in a surface of Euler genus g is at most 18√{47g} + O(1), which is asymptotically best possible as it asymptotically differs from the lower bound by a constant multiplicative factor. Our proof also yields a quadratic time algorithm to find a corresponding contraction sequence. To prove the upper bound on twin-width of graphs embeddable in surfaces, we provide a stronger version of the Product Structure Theorem for graphs of Euler genus g that asserts that every such graph is a subgraph of the strong product of a path and a graph with a tree-decomposition with all bags of size at most eight with a single exceptional bag of size max{6, 32g-37}.

Název v anglickém jazyce

Twin-width of graphs on surfaces

Popis výsledku anglicky

Twin-width is a width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS'20, JACM'22], which has many structural and algorithmic applications. Hliněný and Jedelský [ICALP'23] showed that every planar graph has twin-width at most 8. We prove that the twin-width of every graph embeddable in a surface of Euler genus g is at most 18√{47g} + O(1), which is asymptotically best possible as it asymptotically differs from the lower bound by a constant multiplicative factor. Our proof also yields a quadratic time algorithm to find a corresponding contraction sequence. To prove the upper bound on twin-width of graphs embeddable in surfaces, we provide a stronger version of the Product Structure Theorem for graphs of Euler genus g that asserts that every such graph is a subgraph of the strong product of a path and a graph with a tree-decomposition with all bags of size at most eight with a single exceptional bag of size max{6, 32g-37}.

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

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Návaznosti

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 statě ve sborníku

49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

ISBN

9783959773355

ISSN

1868-8969

e-ISSN

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Počet stran výsledku

15

Strana od-do

„66:1“-„66:15“

Název nakladatele

Schloss Dagstuhl – Leibniz-Zentrum für Informatik

Místo vydání

Dagstuhl, Germany

Místo konání akce

Dagstuhl, Germany

Datum konání akce

1. 1. 2024

Typ akce podle státní příslušnosti

CST - Celostátní akce

Kód UT WoS článku

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