An entropy proof of Bergman's theorem
Journal of Combinatorial Theory Series A
On the maximum number of Hamiltonian paths in tournaments
Random Structures & Algorithms
Theory of Information and Coding
Theory of Information and Coding
Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
Hamiltonian Cycles in Regular Tournaments
Combinatorics, Probability and Computing
A survey on Hamilton cycles in directed graphs
European Journal of Combinatorics
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Let $P(n)$ and $C(n)$ denote, respectively, the maximum possible numbers of Hamiltonian paths and Hamiltonian cycles in a tournament on n vertices. The study of $P(n)$ was suggested by Szele [14], who showed in an early application of the probabilistic method that $P(n) \geq n!2^{-n+1}$, and conjectured that $\lim ( {P(n)}/ {n!} )^{1/n}= 1/2.$ This was proved by Alon [2], who observed that the conjecture follows from a suitable bound on $C(n)$, and showed $C(n)