On the maximum number of Hamiltonian paths in tournaments
TLDR
In this article, it was shown that the maximum number of directed Hamiltonian paths in a tournament on n vertices is at mostc · n3/2· n!/2n−1, wherec is a positive constant independent of n.Abstract:
Solving an old conjecture of Szele we show that the maximum number of directed Hamiltonian paths in a tournament onn vertices is at mostc · n3/2· n!/2n−1, wherec is a positive constant independent ofn.read more
Citations
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Problems and results in extremal combinatorics-II
TL;DR: This paper contains a collection of problems and results in the area, including solutions or partial solutions to open problems suggested by various researchers, and is a sequel to a previous paper of the same flavor.
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Advances on the Hamiltonian Problem – A Survey
TL;DR: This article is intended as a survey, updating earlier surveys in the area and contains material on closely related topics such as traceable, pancyclic and hamiltonian-connected graphs and digraphs.
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An updated survey on the linear ordering problem for weighted or unweighted tournaments
Irène Charon,Olivier Hudry +1 more
TL;DR: It is shown how the linear ordering problem can be used to model an aggregation problem consisting of going from individual preferences defined on a set of candidates to a collective ranking of these candidates.
Posted Content
Hamilton cycles in graphs and hypergraphs: an extremal perspective
Daniela Kühn,Deryk Osthus +1 more
TL;DR: The Hamilton cycle problem has been the subject of intensive research as discussed by the authors, with an emphasis on extremal and probabilistic approaches, and a survey of recent developments and open problems can be found in this paper.
Journal ArticleDOI
A survey on the linear ordering problem for weighted or unweighted tournaments
Irène Charon,Olivier Hudry +1 more
TL;DR: It is shown how the linear ordering problem can be used to model an aggregation problem consisting of going from individual preferences defined on a set of candidates to a collective ranking of these candidates.
References
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The Probabilistic Method
TL;DR: A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored.
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Probabilistic Methods in Combinatorics
TL;DR: In this paper, Erdős [8] showed that the probabilistic method must exist for a graph G(n,.5) to be a random graph, and that a graph satisfying ∧( √ B_s) ≠ ∅ must exist.
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Ten lectures on the probabilistic method
TL;DR: The Janson Inequalities as discussed by the authors allow accurate approximation of extremely small probabilities, and have been shown to be useful for the probabilistic method in many problems. But they do not cover the complexity of the Janson inequalities.
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Upper bounds for permanents of $\left( {0,\,1} \right)$-matrices
TL;DR: In this paper, a printing device of the type having a carriage which supports a printing roll is described, where the carriage is pivotally and slidably mounted on a slide rod.
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A short proof of Minc's conjecture
TL;DR: A short proof is given of the following conjecture of Minc: a n × n − (0, 1)-matrix with ri ones in row i = 1 n r i !