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1 results

  • Size, Order, and Connected Domination

  • Simon Mukwembi
  • Journal:
    Canadian Mathematical Bulletin / Volume 57 / Issue 1 / 14 March 2014
    Published online by Cambridge University Press:
    20 November 2018, pp. 141-144
    Print publication:
    14 March 2014
    • Article
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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.