SUFFICIENT CONDITION FOR THE EXISTENCE OF THREE DISJOINT THETA GRAPHS

Title & Authors
SUFFICIENT CONDITION FOR THE EXISTENCE OF THREE DISJOINT THETA GRAPHS
Gao, Yunshu; Ma, Ding;

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 $\small{n{\geq}12}$ and size at least $\small{{\lfloor}\frac{11n-18}{2}{\rfloor}}$ contains three disjoint theta graphs. As a corollary, every graph of order $\small{n{\geq}12}$ and size at least $\small{{\lfloor}\frac{11n-18}{2}{\rfloor}}$ contains three disjoint cycles of even length.
Keywords
disjoint theta graphs;sufficient condition;minimum degree;
Language
English
Cited by
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