Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Esperet, Louis; Norin, Sergey https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
when quoting this document, please refer to the following
DOI:
URN: urn:nbn:de:0030-drops-163997
URL:

;

Testability and Local Certification of Monotone Properties in Minor-Closed Classes

pdf-format:


Abstract

The main problem in the area of graph property testing is to understand which graph properties are testable, which means that with constantly many queries to any input graph G, a tester can decide with good probability whether G satisfies the property, or is far from satisfying the property. Testable properties are well understood in the dense model and in the bounded degree model, but little is known in sparse graph classes when graphs are allowed to have unbounded degree. This is the setting of the sparse model.
We prove that for any proper minor-closed class 𝒢, any monotone property (i.e., any property that is closed under taking subgraphs) is testable for graphs from 𝒢 in the sparse model. This extends a result of Czumaj and Sohler (FOCS'19), who proved it for monotone properties with finitely many forbidden subgraphs. Our result implies for instance that for any integers k and t, k-colorability of K_t-minor free graphs is testable in the sparse model.
Elek recently proved that monotone properties of bounded degree graphs from minor-closed classes that are closed under disjoint union can be verified by an approximate proof labeling scheme in constant time. We show again that the assumption of bounded degree can be omitted in his result.

BibTeX - Entry

@InProceedings{esperet_et_al:LIPIcs.ICALP.2022.58,
  author =	{Esperet, Louis and Norin, Sergey},
  title =	{{Testability and Local Certification of Monotone Properties in Minor-Closed Classes}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{58:1--58:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16399},
  URN =		{urn:nbn:de:0030-drops-163997},
  doi =		{10.4230/LIPIcs.ICALP.2022.58},
  annote =	{Keywords: Property testing, sparse model, local certification, minor-closed classes}
}

Keywords: Property testing, sparse model, local certification, minor-closed classes
Seminar: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue date: 2022
Date of publication: 28.06.2022


DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI