Problem

Source: Mongolia TST 2011 Test 2 #3

Tags: inequalities, pigeonhole principle, combinatorics unsolved, combinatorics



Let $G$ be a graph, not containing $K_4$ as a subgraph and $|V(G)|=3k$ (I interpret this to be the number of vertices is divisible by 3). What is the maximum number of triangles in $G$?