Girth of {C-3, ... , C-s}-free extremal graphs
Let G be a {C3, . . . , Cs}-free graph with as many edges as possible. In this paper we consider a question studied by several authors, the compulsory existence of the cycle Cs+1 in G. The answer has already been proved to be affirmative for s = 3, 4, 5, 6. In this work we show that the girth of G i...
| Autores: | , , |
|---|---|
| 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:11441/163509 |
| Acceso en línea: | https://hdl.handle.net/11441/163509 https://doi.org/10.1016/j.dam.2012.01.020 |
| Access Level: | acceso abierto |
| Palabra clave: | Extremal graph Extremal function Girth Degree of an edge |
| Sumario: | Let G be a {C3, . . . , Cs}-free graph with as many edges as possible. In this paper we consider a question studied by several authors, the compulsory existence of the cycle Cs+1 in G. The answer has already been proved to be affirmative for s = 3, 4, 5, 6. In this work we show that the girth of G is g(G) = s+1 when the order of G is at least 1+ s s−2 2 s−2 −4 s−4 if s is even, and 1 + (s−1) 3 (s−2) 2−1 4 s−3 2 −8s 2(s−2) 2−10 if s is odd. This bound is an improvement of the best general result so far known. Moreover, we also prove in the case s = 7 that the girth is g(G) = 8 for order at least 14 and characterize all the extremal graphs whose girth is not 8 |
|---|