On the minimal monochromatic K4-density

Details On the minimal monochromatic K4-density On the minimal monochromatic K4-density

2011-06-06

arxiv.org/abs/1106.1030v4

Mathematics

Combinatorics

Scientific paper

We use Razborov's flag algebra method to show a new asymptotic lower bound
for the minimal density $m_4$ of monochromatic $K_4$'s in any 2-coloring of the
edges of the complete graph $K_n$ on $n$ vertices. The hitherto best known
lower bound was obtained by Giraud, who proved that m_4>1/46, whereas the best
known upper bound by Thomason states that m_4<1/33. We can show that m_4>1/35.

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