On endomorphism universality of sparse graph classes.

We show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best-possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids amo...

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Detalles Bibliográficos
Autores: Knauer, Kolja, Puig i Surroca, G.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad de Oviedo (UNIOVI)
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/227127
Acceso en línea:https://hdl.handle.net/2445/227127
Access Level:acceso abierto
Palabra clave:Isomorfismes (Matemàtica)
Teoria de grafs
Representacions de semigrups
Isomorphisms (Mathematics)
Graph theory
Representations of semigroups
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spelling On endomorphism universality of sparse graph classes.Knauer, KoljaPuig i Surroca, G.Isomorfismes (Matemàtica)Teoria de grafsRepresentacions de semigrupsIsomorphisms (Mathematics)Graph theoryRepresentations of semigroupsWe show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best-possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids. As a by-product, we prove that monoids can be represented by graphs of bounded expansion (reproving a result of Nešetřil and Ossona de Mendez) and $k$-cancellative monoids can be represented by graphs of bounded degree. Finally, we show that not all completely regular monoids can be represented by graphs excluding topological minor (strengthening a result of Babai and Pultr).Wiley2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/227127Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de Oviedo (UNIOVI)InglésReproducció del document publicat a: https://doi.org/10.1002/jgt.23262Journal of Graph Theory, 2025, vol. 110, num.2, p. 223-244https://doi.org/10.1002/jgt.23262cc by-nc-nd (c) Kolja Knauer et al., 2025http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2271272026-05-27T06:46:51Z
dc.title.none.fl_str_mv On endomorphism universality of sparse graph classes.
title On endomorphism universality of sparse graph classes.
spellingShingle On endomorphism universality of sparse graph classes.
Knauer, Kolja
Isomorfismes (Matemàtica)
Teoria de grafs
Representacions de semigrups
Isomorphisms (Mathematics)
Graph theory
Representations of semigroups
title_short On endomorphism universality of sparse graph classes.
title_full On endomorphism universality of sparse graph classes.
title_fullStr On endomorphism universality of sparse graph classes.
title_full_unstemmed On endomorphism universality of sparse graph classes.
title_sort On endomorphism universality of sparse graph classes.
dc.creator.none.fl_str_mv Knauer, Kolja
Puig i Surroca, G.
author Knauer, Kolja
author_facet Knauer, Kolja
Puig i Surroca, G.
author_role author
author2 Puig i Surroca, G.
author2_role author
dc.subject.none.fl_str_mv Isomorfismes (Matemàtica)
Teoria de grafs
Representacions de semigrups
Isomorphisms (Mathematics)
Graph theory
Representations of semigroups
topic Isomorfismes (Matemàtica)
Teoria de grafs
Representacions de semigrups
Isomorphisms (Mathematics)
Graph theory
Representations of semigroups
description We show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best-possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids. As a by-product, we prove that monoids can be represented by graphs of bounded expansion (reproving a result of Nešetřil and Ossona de Mendez) and $k$-cancellative monoids can be represented by graphs of bounded degree. Finally, we show that not all completely regular monoids can be represented by graphs excluding topological minor (strengthening a result of Babai and Pultr).
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/227127
url https://hdl.handle.net/2445/227127
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1002/jgt.23262
Journal of Graph Theory, 2025, vol. 110, num.2, p. 223-244
https://doi.org/10.1002/jgt.23262
dc.rights.none.fl_str_mv cc by-nc-nd (c) Kolja Knauer et al., 2025
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by-nc-nd (c) Kolja Knauer et al., 2025
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Oviedo (UNIOVI)
instname_str Universidad de Oviedo (UNIOVI)
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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