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# Tournaments and King Chickens

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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: