Jest Exam

Question

A tournament is a directed graph in which there is exactly one directed edge between
every pair of vertices. Let Tn be a tournament on n vertices.
(a) Use induction to prove the following statement:
Tn has a directed hamiltonian path (a directed path that visits all vertices).
(b) Describe an algorithm that finds a directed hamiltonian path in a given tourna-
ment. Do not write whole programs; pseudocode, or a simple description of the
steps in the algorithm, will suffice. What is the worst case time complexity of
your algorithm?