An upper bound for the arrow-simplicity s(T) of a tournament T

Abderrahim Boussairi; Imane Talbaoui; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 253

An upper bound for the arrow-simplicity s(T) of a tournament T

Abderrahim Boussairi, Imane Talbaoui

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Feb 01, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: The arrow-simplicity s(T) of a tournament T is the minimum number of arcs that must be reversed to make T non simple. V. Müller et J. Pelant [1] prove that s(T)=((n-1)/2) if and only if T is doubly regular. Recall that a n-tournament T is doubly regular if there is an integer k such that every pair of vertices of T dominates exactly k vertices. If such tournament exists then n≡3mod(4) and k=((n-3)/4). In this work, we give an upper bound for the arrow-simplicity s(T) of a tournament T where T is an n-tournaments and n≢3mod(4). Keywords: