Sufficient condition for the existence of three disjoint theta graphs
Bull. Korean Math. Soc. 2015 Vol. 52, No. 1, 287-299
https://doi.org/10.4134/BKMS.2015.52.1.287
Printed January 31, 2015
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.
Keywords : disjoint theta graphs, sufficient condition, minimum degree
MSC numbers : 05C35, 05C70
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