Triangle-intersecting families on eight vertices

Details Triangle-intersecting families on eight vertices Triangle-intersecting families on eight vertices

2011-02-09

arxiv.org/abs/1102.1764v1

Mathematics

Combinatorics

Scientific paper

Simonovits and S\'{o}s conjectured that the maximal size of a
triangle-intersecting family of graphs on $n$ vertices is $2^{\binom{n}{2}-3}$.
Their conjecture has recently been proved using spectral methods. We provide an
elementary proof of the special case of $8$ vertices using a partition
argument.

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