Tournaments and King Chickens

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:

“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: