Topological minors in bipartite graphs
For a bipartite graph G on m and n vertices, respectively, in its vertices classes, and for integers s and t such that 2 ≤ s ≤ t, 0 ≤ m − s ≤ n − t, and m + n ≤ 2s + t − 1, we prove that if G has at least mn − (2(m − s) + n − t) edges then it contains a subdivision of the complete bipartite K(s,t) w...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/154130 |
| Acceso en línea: | https://hdl.handle.net/11441/154130 https://doi.org/10.1007/s10114-011-0149-x |
| Access Level: | acceso abierto |
| Palabra clave: | bipartite graphs extremal graph theory topological minor |
| Sumario: | For a bipartite graph G on m and n vertices, respectively, in its vertices classes, and for integers s and t such that 2 ≤ s ≤ t, 0 ≤ m − s ≤ n − t, and m + n ≤ 2s + t − 1, we prove that if G has at least mn − (2(m − s) + n − t) edges then it contains a subdivision of the complete bipartite K(s,t) with s vertices in the m-class and t vertices in the n-class. Furthermore, we characterize the corresponding extremal bipartite graphs with mn−(2(m−s)+n−t+ 1) edges for this topological Turan type problem. |
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