Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
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 Reviewed
Postprint (author's final draft)
Article
English
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
https://www.sciencedirect.com/science/article/abs/pii/S0012365X19300627
Open Access
E-prints [72986]
