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 Citació: Abajo, E.; Balbuena, C.; Diánez, A. New families of graphs without short cycles and large size. "Discrete applied mathematics", 06 Juny 2010, vol. 158, núm. 11, p. 1127-1135. Títol: New families of graphs without short cycles and large size Autor: Abajo, E.; Balbuena Martínez, Maria Camino Teófila ; Diánez, A. Data: 6-jun-2010 Tipus de document: Article Resum: We denote by ex $(n; {C^3,C^4,…Cs})$ or fs(n) the maximum number of edges in a graph of order n and girth at least s+1. First we give a method to transform an n-vertex graph of girth g into a graph of girth at least g-1 on fewer vertices. For an infinite sequence of values of n and s∈{4, 6, 10} the obtained graphs are denser than the known constructions of graphs of the same girth s+1. We also give another different construction of dense graphs for an infinite sequence of values of n and s∈{7, 11}. These two methods improve the known lower bounds on fs(n) for s ∊ {4, 6, 7, 10, 11} which were obtained using different algorithms. Finally, to know how good are our results, we have proved that $\limsup_{n\longrightarrow{\infty}}\displaystyle\frac{\int_s (n)}{n^{1+\displaystyle\frac{2}{s-1}}}=2^{-1-\displaystyle\frac{2}{s-1}}$ for s ∊ 2 {5, 7, 11}, and $s^{-1-\displaystyle\frac{2}{s}}$ ≤ $\limsup_{n\longrightarrow{\infty}}\displaystyle\frac{\int_s (n)}{n^{1+\displaystyle\frac{2}{s}}}$ ≤ 0.5 for s ∊ {6, 10}. ISSN: 0166-218X URI: http://hdl.handle.net/2117/8745 DOI: 10.1016/j.dam.2010.03.007 Versió de l'editor: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TYW-4YVP0YS-1-7&_cdi=5629&_user=1517299&_pii=S0166218X10001010&_origin=search&_coverDate=06%2F06%2F2010&_sk=998419988&view=c&wchp=dGLbVzW-zSkWA&md5=c43b16d712df6f26a42049cc194da9de&ie=/sdarticle.pdf Apareix a les col·leccions: COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions. Articles de revistaDepartaments de Matemàtica Aplicada. Articles de revistaAltres. Enviament des de DRAC Comparteix: