Forbidding Couples of Tournaments and the Erdös–Hajnal Conjecture

A celebrated unresolved conjecture of Erdös and Hajnal states that for every undirected graph H there exists $$ \epsilon (H) > 0 such on n vertices does not contain as an induced subgraph contains a clique or stable set size at least n^{\epsilon (H)} . This has directed equivalent version stating tournament H-free n-vertex T transitive subtournament Recently the was proved all six-vertex tournaments, except $$K_{6}$$ In this paper we construct two infinite families tournaments which is still open infinitely many in these families—the family so-called super nebulas triangular galaxies. We prove nebula $$H_{1}$$ $$\varDelta galaxy $$H_{2}$$ exist $$\epsilon (H_{1},H_{2})$$ $$\lbrace H_{1},H_{2}\rbrace -free $$\mid \mid ^{\epsilon (H_{1},H_{2})}$$ also central (K_{6},H)$$ K_{6},H\rbrace (K_{6},H)}$$ And give extension our results.