Sufficient condition for the existence of three disjoint theta graphs

摘要

A theta graph is the union of three internally disjoint paths that have the same two distinct end vertices. We show that every graph of order $n geq 12$ and size at least $lfloorrac{11n-18}{2}floor$ contains three disjoint theta graphs. As a corollary, every graph of order $ngeq 12$ and size at least $lfloorrac{11n-18}{2}floor$ contains three disjoint cycles of even length.