Exact values of ex(v; {C-3, C-4, ... , C-n})

For integers n ≥ 4 and ν ≥ n+1, let ex(ν; {C3, C4, . . . , Cn}) denote the maximum number of edges in a graph with ν vertices and girth at least n + 1. In this paper we have obtained bounds on this function for n ∈ {5, 6, 7} and, in several cases, even the exact value. We have also developed a greed...

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Bibliographic Details
Authors: Abajo Casado, María Encarnación, Diánez Martínez, Ana Rosa
Format: article
Status:Versión aceptada para publicación
Publication Date:2010
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/163487
Online Access:https://hdl.handle.net/11441/163487
https://doi.org/10.1016/j.dam.2010.08.002
Access Level:Open access
Keyword:Extremal graphs
Girth
Cages
Description
Summary:For integers n ≥ 4 and ν ≥ n+1, let ex(ν; {C3, C4, . . . , Cn}) denote the maximum number of edges in a graph with ν vertices and girth at least n + 1. In this paper we have obtained bounds on this function for n ∈ {5, 6, 7} and, in several cases, even the exact value. We have also developed a greedy algorithm for generating graphs with large size for given order and girth.