Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SUFFICIENT CONDITION FOR THE EXISTENCE OF THREE DISJOINT THETA GRAPHS

  • Gao, Yunshu (School of Mathematics and Computer Science Ningxia University) ;
  • Ma, Ding (School of Mathematics and Computer Science Ningxia University)
  • Received : 2014.02.05
  • Published : 2015.01.31
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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.

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Acknowledgement

Supported by : National Natural Science Foundation of China

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