2026-04-17T17:12:07Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/4595142026-03-26T07:48:13Zcom_2072_1033col_2072_452950

Rainbow connectivity of multilayered random geometric graphs Díaz Cort, Josep Diner, Oznur Y. Serra Albó, Oriol Serna Iglesias, María José Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. Departament de Ciències de la Computació Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics Universitat Politècnica de Catalunya. ALBCOM - Algorísmia, Bioinformàtica, Complexitat i Mètodes Formals Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta Classificació AMS::05 Combinatorics::05C Graph theory An edge-colored multigraph G is rainbow connected if every pair of vertices is joined by at least one rainbow path, i.e., a path where no two edges are of the same color. In the context of multilayered networks, we introduce the notion of multilayered random geometric graphs, from h = 2 independent random geometric graphs G(n,r) on the unit square. We define an edge-coloring by coloring the edges according to the copy of G(n,r) they belong to and study the rainbow connectivity of the resulting edge-colored multigraph. We show that r(n) = lnn nh-1 1/2h , is a threshold of the radius for the property of being rainbow connected. This complements the known analogous results for the multilayered graphs defined on the Erdos–Rényi random model. Peer Reviewed Postprint (published version) 2024 Conference report Diaz, J. [et al.]. Rainbow connectivity of multilayered random geometric graphs. A: Discrete Mathematics Days. «DMD 2024: Discrete Mathematics Days: Alcalá de Henares, Espanya, Julio 3-5, 2024». Alcalá de Henares: Universidad de Alcalá, 2024, p. 160-165. ISBN 978-84-18979-38-5. 978-84-18979-38-5 https://hdl.handle.net/2117/459514 https://hdl.handle.net/2117/459514 eng https://dmd2024.web.uah.es/files/abstracts/paper_29.pdf info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-112581GB-C21/ES/MODELOS Y TECNICAS PARA EL PROCESAMIENTO DE INFORMACION A GRAN ESCALA -- BARCELONA/ info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113082GB-I00/ES/COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES/ http://creativecommons.org/licenses/by-nc-sa/4.0/ Open Access Attribution-NonCommercial-ShareAlike 4.0 International 6 p. application/pdf Universidad de Alcalá