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  • Tournaments and King Chickens

    http://www.zabihah.com/biz/7d3Lo4PK8b

    Discrete Math has a lot of weird terms to describe things. This blog post will be no exception where we will talk about tournaments and king chickents.

    “A tournament is a complete graph where every edge has an orientation. An edge that points from \(i\) to \(j\) can be thought of as player \(i\) defeating player \(j\) in a tournament where everyone plays everyone else in 1 game” (Benjamin, 2009, 80).

    A tournament graph looks like this:

    http://www.laboratoryequipment.com/news/2011/03/rock-paper-scissors-explains-ecological-diversity

    “In a tournament, \(x\) is a king chicken (or king) if for every opponent \(y\), either \(x \rightarrow y\) or there exists a player \(z\) such that \(x \rightarrow z \rightarrow y\). In other words, a king is a player that can walk to any vertex in at most 2 steps” (Benjamin, 2009, 81).

    Consider the graph below: