Correction to: A Connection Between Sports and Matroids: How Many Teams Can We Beat?

Abstract

BackgroundOur article "A connection between sports and matroids: How many teams can we beat?" [4] deals with a problem we called MinStanding(S). The motivation behind this problem comes from the following situation. Given an ongoing sports competition among a set T of teams, with each team having a current score and some matches left to be played, we ask whether it is possible for our distinguished team t ∈ T to obtain a final standing with at most r teams finishing before t.For a general model that can be applied to various sports competitions, we denoted by S the set of all possible outcomes of a match, where each outcome is a pair ( p 1 , p 2 ) of non-negative reals corresponding to the situation where the match ends with the home team obtaining p 1 points and the away team obtaining p 2 points. If S contains pairs (α, 0) and (0, β) for some positive α and β, then we say that S is well based.Given a set S of outcomes with |S| = k + 1, the above question boils down to the following graph labelling problem:The online version of the original article can be found under