Exact value of ex(n; {C-3, . . . , C-s}) for n <= [25(s-1)/8]
For integers s ≥ 8 and s+1 ≤ n ≤ ⌊ 25(s−1) 8 ⌋, we determine the exact value of the function ex(n; {C3, . . . , Cs}), that represents the maximum number of edges in a {C3, . . . , Cs}-free graph of order n. This result was already known when 3 ≤ s ≤ 7. To do that, for 1 ≤ k ≤ 5, we provide a family...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2015 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/163395 |
| Acesso em linha: | https://hdl.handle.net/11441/163395 https://doi.org/10.1016/j.dam.2014.11.021 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Extremal function Extremal graphs Forbidden cycles Girth |
| Resumo: | For integers s ≥ 8 and s+1 ≤ n ≤ ⌊ 25(s−1) 8 ⌋, we determine the exact value of the function ex(n; {C3, . . . , Cs}), that represents the maximum number of edges in a {C3, . . . , Cs}-free graph of order n. This result was already known when 3 ≤ s ≤ 7. To do that, for 1 ≤ k ≤ 5, we provide a family of graphs Hk s such that e(Hk s ) − n(Hk s ) = k and with the property that Hk s reaches girth s+1 with the minimum number of vertices. Also, we determine an infinity family of solutions of the problem ex(n; {C3, . . . , Cs}) = n + 6. |
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