Note on eccentricities in tournaments (Q1340121)

The eccentricity \(e_ u\) of a node \(u\) of a tournament \(T_ n\) with \(n\) labelled nodes is the maximum distance from \(u\) to any other node of \(T_ n\). A sequence \((e_ 1,\dots, e_ n)\) is \(e\)-realizable if there exists a tournament \(T_ n\) in which node \(i\) has eccentricity \(e_ i\) for \(1\leq i\leq n\). A sequence \((b_ 1,\dots, b_{n-1})\) is \(b\)- realizable if there exists a tournament \(T_ n\) with \(b_ k\) nodes of eccentricity \(k\) for \(1\leq k\leq n-1\). The authors characterize \(e\)- realizable and \(b\)-realizable sequences.