SUFFICIENT CONDITION FOR THE EXISTENCE OF THREE DISJOINT THETA GRAPHS
Yunshu Gao, Ding Ma · Bulletin of the Korean Mathematical Society · 2015
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 ${\lfloor}\frac{11n-18}{2}{\rfloor}$ contains three disjoint theta graphs. As a corollary, every graph of order $n{\geq}12$ and size at least ${\lfloor}\frac{11n-18}{2}{\rfloor}$ contains three disjoint cycles of even length.