@article {IOPORT.05014316, author = {Alon, Noga and Sudakov, Benny}, title = {$H$-free graphs of large minimum degree.}, year = {2006}, journal = {The Electronic Journal of Combinatorics [electronic only]}, volume = {13}, number = {1}, issn = {1077-8926}, pages = {Research paper R19, 9 p.}, publisher = {Prof. Andr\'e K\"undgen, Deptartment of Mathematics, California State University San Marcos, San Marcos, CA}, abstract = {Summary: We prove the following extension of an old result of {\it B. Andr\'asfai, P. Erd\H{o}s} and {\it V. S\'os} [Discrete Math. 8, 205--218 (1974; Zbl 0284.05106)]. For every fixed graph $H$ with chromatic number $r+1 \geq 3$, and for every fixed $\varepsilon>0$, there are $n_0=n_0(H,\varepsilon)$ and $\rho=\rho(H) >0$, such that the following holds. Let $G$ be an $H$-free graph on $n>n_0$ vertices with minimum degree at least $(1-{1\over r-1/3}+\varepsilon)n$. Then one can delete at most $n^{2-\rho}$ edges to make $G$ $r$-colorable.}, identifier = {05014316}, }