Determining the results of tournament games using complete graphs generation

DAMKHI M., Pehlivan H.

COMPUTATIONAL & APPLIED MATHEMATICS, vol.37, no.5, pp.6198-6211, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.1007/s40314-018-0688-1
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.6198-6211


Sport tournaments usually hold a standings table derived from the results and/or scores of the games. For football tournaments, the table data obviously include the number of wins (W), draws (D) and losses (L), as well as the number of goals for and against. This paper explores all possible results of the games involved in a football tournament based on generating all the complete graphs which match the data in its final table. With the values W, D and L of the teams, it is quite possible to find the tournament graph. However, there might be many different tournament graphs, especially when the tournament involves four or more teams. We evaluate a distinct solution approach by applying it to the table data of a qualifying group from previous FIFA World Cup Group Stages. The approach is expressed with pseudo code and its results is presented with respect to some particular data in the final tables of the tournaments contested by up to ten teams.