2026-04-13T06:56:30Zhttps://recercat.cat/oai/requestoai:recercat.cat:2117/1848692026-02-09T06:46:18Zcom_2072_1033col_2072_452950
RECERCAT
author
Abajo Casado, Encarnación
author
Balbuena Martínez, Maria Camino Teófila
author
Bendala García, Manuel Francisco
author
Marcote Ordax, Francisco Javier
2019-10-01
© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A -graph is a -regular graph with girth and a -cage is a -graph with the fewest possible number of vertices . Constructing -cages and determining the order are both very hard problems. For this reason, an intensive line of research is devoted to constructing smaller -graphs than previously known ones, providing in this way new upper bounds to each time such a graph is constructed. The paper focuses on girth , where cages are known only for degrees . We construct -graphs using and extending techniques of amalgamation into the incidence graphs of elliptic semiplanes of type introduced and exposed by Funk (2009). The order of these graphs provides better upper bounds on than those known so far, for values of such that either or.Peer ReviewedPostprint (author's final draft)
Open Access
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
Combinatorial analysis
Differential equations, Elliptic
Small regular graphs
Cage
Girth
Amalgam
Elliptic semiplane
Combinacions (Matemàtica)
Equacions diferencials el·líptiques
Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
Improving bounds on the order of regular graphs of girth 5
Article