Cera López, MartínDiánez Martínez, Ana RosaMárquez Pérez, Alberto2016-02-092016-02-092004http://hdl.handle.net/11441/34387The exact values of the function $ex(n;TK_{p})$ are known for ${\lceil \frac{2n+5}{3}\rceil}\leq p < n$ (see [Cera, Diánez, and Márquez, SIAM J. Discrete Math., 13 (2000), pp. 295--301]), where $ex(n;TK_p)$ is the maximum number of edges of a graph of order n not containing a subgraph homeomorphic to the complete graph of order $p.$ In this paper, for ${\lceil \frac{2n+6}{3} \rceil}\leq p < n - 3,$ we characterize the family of extremal graphs $EX(n;TK_{p}),$ i.e., the family of graphs with n vertices and $ex(n;TK_{p})$ edges not containing a subgraph homeomorphic to the complete graph of order $p.$application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/extremal graph theorytopological complete subgraphsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1137/S0895480100378677