# Disjoint edge triangles in a complete graph [duplicate]

Possible Duplicate:
Maximum number of distinct 3-cliques in a complete graph

What is the number of disjoint edge triangles in a complete graph. For example, if I have a complete graph on 4 vertices, the number of disjoint edge triangles is 2. How do I extend this to a complete graph of n vertices? every edge is in exactly one triangle.

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## marked as duplicate by Douglas S. Stones, Alexander Gruber♦, Fabian, Davide Giraudo, Chris EagleDec 31 '12 at 12:15

When you say disjoint, do you allow the triangles to have vertices in common? And how do you get two disjoint edge triangles in $K_4$, even if you do allow common vertices? There are only six edges, and if three of them form a triangle, the remaining three don’t. –  Brian M. Scott Oct 14 '12 at 22:25
Any two triangles in $K_4$ have an edge in common, so the maximum number of edge-disjoint triangles in $K_4$ is $1$, not $2$. –  Brian M. Scott Oct 14 '12 at 22:34