The maximum number of Hamiltonian paths in tournaments

DOI10.1007/BF02128667zbMath0724.05036MaRDI QIDQ2276976

Noga Alon

Publication date: 1990

Published in: Combinatorica (Search for Journal in Brave)

zbMATH Keywords

permanentstournamentsmaximum number(0,1)-matricesapplication of Minc's conjectureHamiltonian directed paths

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Paths and cycles (05C38) Directed graphs (digraphs), tournaments (05C20)

Related Items (15)

A survey on the linear ordering problem for weighted or unweighted tournaments ⋮ Some remarks on \((k-1)\)-critical subgraphs of \(k\)-critical graphs ⋮ Counting and packing Hamilton cycles in dense graphs and oriented graphs ⋮ What Moser <em>Could</em> Have Asked: Counting Hamilton Cycles in Tournaments ⋮ The number of Hamiltonian decompositions of regular graphs ⋮ About the number of oriented Hamiltonian paths and cycles in tournaments ⋮ A survey on Hamilton cycles in directed graphs ⋮ Paths of given length in tournaments ⋮ On the Maximum Number of Spanning Copies of an Orientation in a Tournament ⋮ On testing Hamiltonicity of graphs ⋮ On the maximum number of Hamiltonian paths in tournaments ⋮ An updated survey on the linear ordering problem for weighted or unweighted tournaments ⋮ Enumeration of labeled and unlabeled Hamiltonian cycles in complete \(k\)-partite graphs ⋮ About the number of directed paths in tournaments ⋮ Hamiltonian cycles above expectation in \(r\)-graphs and quasi-random \(r\)-graphs

Cites Work

• A short proof of Minc's conjecture
• Upper bounds for permanents of $\left( {0,\,1} \right)$-matrices
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