Sufficient condition for the existence of three disjoint theta graphs

Yunshu Gao; Ding Ma

doi:10.4134/BKMS.2015.52.1.287

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(1): 287-299

Printed January 31, 2015

https://doi.org/10.4134/BKMS.2015.52.1.287

Sufficient condition for the existence of three disjoint theta graphs

Yunshu Gao and Ding Ma

Ningxia University, Ningxia University

Abstract

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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