Graphs with maximum size and lower bounded girth
For integers n ≥ 4 and ν ≥ n + 1, let ex(ν; {C3, . . . , Cn}) denote the maximum number of edges in a graph of order ν and girth at least n+1. The {C3, . . . , Cn}-free graphs with order ν and size ex(ν; {C3, . . . , Cn}) are called extremal graphs and denoted by EX(ν; {C3, . . . , Cn}). We prove th...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/163658 |
| Acceso en línea: | https://hdl.handle.net/11441/163658 https://doi.org/10.1016/j.aml.2011.09.062 |
| Access Level: | acceso abierto |
| Palabra clave: | Extremal function Extremal graphs Forbidden cycles Girth Cages |
| Sumario: | For integers n ≥ 4 and ν ≥ n + 1, let ex(ν; {C3, . . . , Cn}) denote the maximum number of edges in a graph of order ν and girth at least n+1. The {C3, . . . , Cn}-free graphs with order ν and size ex(ν; {C3, . . . , Cn}) are called extremal graphs and denoted by EX(ν; {C3, . . . , Cn}). We prove that given an integer k ≥ 0, for each n ≥ 2 log2 (k + 2) there exist extremal graphs with ν vertices, ν + k edges and minimum degree 1 or 2. Considering this idea we construct four infinite families of extremal graphs. We also see that minimal (r; g)-cages are the exclusive elements in EX(ν0(r, g); {C3, . . . , Cg−1}). |
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