Yunshu Gao and Ding Ma Ningxia University, Ningxia University

Abstract : 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.