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Size, Order, and Connected Domination

Published online by Cambridge University Press:  20 November 2018

Simon Mukwembi
Simon Mukwembi*
Affiliation:
University of KwaZulu-Natal, Durban, South Africa e-mail: mukwembi@ukzn.ac.za
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Abstract

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We give a sharp upper bound on the size of a triangle-free graph of a given order and connected domination. Our bound, apart from strengthening an old classical theorem of Mantel and of Turán improves on a theorem of Sanchis. Further, as corollaries, we settle a long standing conjecture of Graffiti on the leaf number and local independence for triangle-free graphs and answer a question of Griggs, Kleitman, and Shastri on a lower bound of the leaf number in triangle-free graphs.

Keywords

05C69sizeconnected dominationlocal independence numberleaf number

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 141 - 144
Copyright
Copyright © Canadian Mathematical Society 2014

References

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