caa a22 4500 44581361X CHVBK 20180317145219.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s11083-010-9155-3 doi (NATIONALLICENCE)springer-10.1007/s11083-010-9155-3 Maximum Distance Between Slater Orders and Copeland Orders of Tournaments [Elektronische Daten] [Irène Charon, Olivier Hudry] Given a tournament T = (X, A), we consider two tournament solutions applied to T: Slater's solution and Copeland's solution. Slater's solution consists in determining the linear orders obtained by reversing a minimum number of directed edges of T in order to make T transitive. Copeland's solution applied to T ranks the vertices of T according to their decreasing out-degrees. The aim of this paper is to compare the results provided by these two methods: to which extent can they lead to different orders? We consider three cases: T is any tournament, T is strongly connected, T has only one Slater order. For each one of these three cases, we specify the maximum of the symmetric difference distance between Slater orders and Copeland orders. More precisely, thanks to a result dealing with arc-disjoint circuits in circular tournaments, we show that this maximum is equal to n(n − 1)/2 if T is any tournament on an odd number n of vertices, to (n 2 − 3n + 2)/2 if T is any tournament on an even number n of vertices, to n(n − 1)/2 if T is strongly connected with an odd number n of vertices, to (n 2 − 3n − 2)/2 if T is strongly connected with an even number n of vertices greater than or equal to 8, to (n 2 − 5n + 6)/2 if T has an odd number n of vertices and only one Slater order, to (n 2 − 5n + 8)/2 if T has an even number n of vertices and only one Slater order. Springer Science+Business Media B.V., 2010 Majority tournament nationallicence Tournament solutions nationallicence Slater orders nationallicence Slaterwinners nationallicence Copeland orders nationallicence Copeland winners nationallicence Symmetricdifferencedistance nationallicence Arc-disjoint circuits in circular tournaments nationallicence Charon Irène Télécom ParisTech, 46, rue Barrault, 75634, Paris Cedex 13, France aut Hudry Olivier Télécom ParisTech, 46, rue Barrault, 75634, Paris Cedex 13, France aut Order Springer Netherlands 28/1(2011-03-01), 99-119 0167-8094 28:1<99 2011 28 11083 https://doi.org/10.1007/s11083-010-9155-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9155-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Charon Irène Télécom ParisTech, 46, rue Barrault, 75634, Paris Cedex 13, France aut NATIONALLICENCE 700 1- Hudry Olivier Télécom ParisTech, 46, rue Barrault, 75634, Paris Cedex 13, France aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/1(2011-03-01), 99-119 0167-8094 28:1<99 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer