ON THE ERDOS-HAJNAL PROBLEM FOR 3-GRAPHS

摘要

Let m(n, r) be the minimal number of edges of an n-uniform hypergraph which is not r-colorable. It is known that for a fixed n, the sequence m(n, r)/rn has a limit. The only trivial case is n = 2 in which m2r=r+12.documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ mleft(2,right)=left(underset{2}{r+1}ight). $$end{document} The goal of this note is to improve a known lower bound for m(3, r).