1. CMB 2013 (vol 57 pp. 141)
|Size, Order, and Connected Domination|
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 TurÃ¡n , 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:size, connected domination, local independence number, leaf number