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Extremal Graphs without Topological Complete Subgraphs

 

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Author: Cera López, Martín
Diánez Martínez, Ana Rosa
Márquez Pérez, Alberto
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2004
Published in: SIAM J. Discrete Math., 18(2),(2004), pp. 388–396.
Document type: Article
Abstract: The 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 $p.$
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URI: http://hdl.handle.net/11441/34387

DOI: http://dx.doi.org/10.1137/S0895480100378677

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