On the maximum number of Hamiltonian paths in tournaments
نویسندگان
چکیده
By using the probabilistic method, we show that the maximum number of directed Hamiltonian paths in a complete directed graph with n vertices is at least (e− o(1)) n! 2n−1 .
منابع مشابه
The maximum number of Hamiltonian paths in tournaments
Solving an old conjecture of Szele we show that the maximum number of directed Hamiltonian paths in a tournament on n vertices is at most c · n · n! 2n−1 , where c is a positive constant independent of n.
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Let $T$ be a non-trivial tournament. An arc is emph{$t$-pancyclic} in $T$, if it is contained in a cycle of length $ell$ for every $tleq ell leq |V(T)|$. Let $p^t(T)$ denote the number of $t$-pancyclic arcs in $T$ and $h^t(T)$ the maximum number of $t$-pancyclic arcs contained in the same Hamiltonian cycle of $T$. Moon ({em J. Combin. Inform. System Sci.}, {bf 19} (1994), 207-214) showed that $...
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ورودعنوان ژورنال:
- Random Struct. Algorithms
دوره 18 شماره
صفحات -
تاریخ انتشار 2001