Transductions of Graph Classes Admitting Product Structure

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F25%3A00142528" target="_blank" >RIV/00216224:14330/25:00142528 - isvavai.cz</a>

Výsledek na webu

<a href="https://arxiv.org/abs/2501.18326" target="_blank" >https://arxiv.org/abs/2501.18326</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/LICS65433.2025.00069" target="_blank" >10.1109/LICS65433.2025.00069</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Transductions of Graph Classes Admitting Product Structure

Popis výsledku v původním jazyce

In a quest to thoroughly understand the first-order transduction hierarchy of hereditary graph classes, some questions in particular stand out; such as, what properties hold for graph classes that are first-order transductions of planar graphs (and of similar classes)? When addressing this (so-far wide open) question, we turn to the concept of a product structure – being a subgraph of the strong product of a path and a graph of bounded tree-width, introduced by Dujmović et al. [JACM 2020]. Namely, we prove that any graph class which is a first-order transduction of a class admitting such product structure, up to perturbations also meets a structural description generalizing the concept of a product structure in a dense hereditary way—the latter concept being introduced just recently by authors under the name of H-clique-width [MFCS 2024].Using this characterization, we show that the class of the 3D grids, as well as a class of certain modifications of 2D grids, are not first-order transducible from classes admitting a product structure, and in particular not from the class of planar graphs.

Název v anglickém jazyce

Transductions of Graph Classes Admitting Product Structure

Popis výsledku anglicky

In a quest to thoroughly understand the first-order transduction hierarchy of hereditary graph classes, some questions in particular stand out; such as, what properties hold for graph classes that are first-order transductions of planar graphs (and of similar classes)? When addressing this (so-far wide open) question, we turn to the concept of a product structure – being a subgraph of the strong product of a path and a graph of bounded tree-width, introduced by Dujmović et al. [JACM 2020]. Namely, we prove that any graph class which is a first-order transduction of a class admitting such product structure, up to perturbations also meets a structural description generalizing the concept of a product structure in a dense hereditary way—the latter concept being introduced just recently by authors under the name of H-clique-width [MFCS 2024].Using this characterization, we show that the class of the 3D grids, as well as a class of certain modifications of 2D grids, are not first-order transducible from classes admitting a product structure, and in particular not from the class of planar graphs.

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

2025

Kód důvěrnosti údajů

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

Název statě ve sborníku

40th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

ISBN

9798331579005

ISSN

1043-6871

e-ISSN

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Počet stran výsledku

13

Strana od-do

843-855

Název nakladatele

IEEE

Místo vydání

USA

Místo konání akce

Singapore, Singapore

Datum konání akce

23. 6. 2025

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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