“In a tournament, x is a king chicken (or king) if for every opponent y, either x Æ y or there exists a player z such that x Æ z Æ y. In other words, a king is a player that can walk to any vertex in at most 2 steps” (Benjamin, 2009, 81). So in the above graph, the following vertices are kings:

1 is a king because \(1\rightarrow 2\), \(1\rightarrow 4\), \(1\rightarrow 2\), \(1\rightarrow 4\rightarrow 3\), and \(1\rightarrow 2\rightarrow 5\).

2 is a king because \(2\rightarrow 5\), \(2\rightarrow 5\rightarrow 1\), \(2\rightarrow 5\rightarrow 3\), and \(2\rightarrow 5\rightarrow 4\).

3 is a king because