
02139187
j
02139187
Cera, M.
Di\'anez, A.
M\'arquez, A.
Extremal graphs without topological complete subgraphs.
SIAM J. Discrete Math. 18, No. 2, 388396 (2004).
2004
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
EN
Zbl 0947.05045
doi:10.1137/S0895480100378677
Summary: The exact values of the function $\text{ex}(n;TK_{p})$ are known for ${\lceil \frac{2n+5}{3}\rceil}\leq p < n$ [see {\it M. Cera, A. Di\'anez}, and {\it A. M\'arquez}, SIAM J. Discrete Math. 13, 295301 (2000; Zbl 0947.05045)], where $\text{ex}(n;TK_p)$ 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 $\text{EX}(n;TK_{p}),$ i.e., the family of graphs with $n$ vertices and $\text{ex}(n;TK_{p})$ edges not containing a subgraph homeomorphic to the complete graph of order $p.$