Note: A tournament of order 14 with disjoint Banks and Slater sets

Authors:
Patric R. J. Östergård;Vesa P. Vaskelainen
Affiliations:
Department of Communications and Networking, Helsinki University of Technology TKK, P.O. Box 3000, 02015 TKK, Finland;Department of Communications and Networking, Helsinki University of Technology TKK, P.O. Box 3000, 02015 TKK, Finland
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

It is shown in this note that there exists a tournament of order 14 with disjoint Banks and Slater sets. Previously, the smallest such tournament was reported to be of order 16. In addition, it is shown that 11 is the minimum order of a tournament in which the Slater set is not a subset of the Banks set.