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Tournaments with many Hamilton cycles

by N. C. Wormald
"... The object of interest is the maximum number, h(n), of Hamilton cycles in an n-tournament. By considering the expected number of Hamilton cycles in various classes of random tournaments, we obtain new asymptotic lower bounds on h(n). The best result so far is approximately 2.85584... times the expec ..."
Abstract - Cited by 6 (0 self) - Add to MetaCart
The object of interest is the maximum number, h(n), of Hamilton cycles in an n-tournament. By considering the expected number of Hamilton cycles in various classes of random tournaments, we obtain new asymptotic lower bounds on h(n). The best result so far is approximately 2.85584... times

Hamilton cycles in quasirandom hypergraphs

by John Lenz, Dhruv Mubayi, Richard Mycroft , 2015
"... We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(nk−1) contains a loose Hamilton cycle. We also give a construction to show that a k-uniform hypergraph satisfying ..."
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We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(nk−1) contains a loose Hamilton cycle. We also give a construction to show that a k-uniform hypergraph satisfying

Voltage Graphs and Hamilton Cycles

by I. Dejter, V. Neumann-Lara , 1991
"... Given a group Zn acting freely on a graph G, the notion of an ordinary voltage graph is applied to the search for Hamilton cycles we of G invariant under an action of Zn on G. As application, for n = 4 and 2, equivalent conditions and lower bounds for chessknight Hamilton cycles containing paths spa ..."
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Given a group Zn acting freely on a graph G, the notion of an ordinary voltage graph is applied to the search for Hamilton cycles we of G invariant under an action of Zn on G. As application, for n = 4 and 2, equivalent conditions and lower bounds for chessknight Hamilton cycles containing paths

Loose Hamilton cycles in hypergraphs

by Peter Keevash, Daniela Kühn, Richard Mycroft, Deryk Osthus , 2008
"... We prove that any k-uniform hypergraph on n vertices with minimum degree n at least + o(n) contains a loose Hamilton cycle. The proof strategy is similar to that 2(k−1) used by Kühn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k-uniform case, our argument her ..."
Abstract - Cited by 5 (1 self) - Add to MetaCart
We prove that any k-uniform hypergraph on n vertices with minimum degree n at least + o(n) contains a loose Hamilton cycle. The proof strategy is similar to that 2(k−1) used by Kühn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k-uniform case, our argument

Hamilton Cycles in the Union of Random Permutations

by Alan Frieze , 1999
"... We prove that two random permutations almost always contain an undirected Hamilton cycle and that three random permutations almost always contain a directed Hamilton cycle. ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
We prove that two random permutations almost always contain an undirected Hamilton cycle and that three random permutations almost always contain a directed Hamilton cycle.

ON COVERING EXPANDER GRAPHS BY HAMILTON CYCLES

by Roman Glebov, Michael Krivelevich, Tibor Szabó , 2012
"... The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree ∆ satisfies some basic expansion properties and contain ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree ∆ satisfies some basic expansion properties

Hamilton cycle decomposition of the Butterfly network

by Jean-Claude Bermond, Eric Darrot, Olivier Delmas, Stephane Perennes , 1996
"... In this paper, we prove that the wrapped Butterfly graph WBF(d;n) of degree d and dimension n is decomposable into Hamilton cycles. This answers a conjecture of D. Barth and A. Raspaud who solved the case d = 2. ..."
Abstract - Cited by 5 (2 self) - Add to MetaCart
In this paper, we prove that the wrapped Butterfly graph WBF(d;n) of degree d and dimension n is decomposable into Hamilton cycles. This answers a conjecture of D. Barth and A. Raspaud who solved the case d = 2.

Multicoloured Hamilton Cycles

by Michael Albert , Alan Frieze, Bruce Reed - ELECTRONIC JOURNAL OF COMBINATORICS , 1995
"... The edges of the complete graph K n are coloured so that no colour appears more than dcne times, where c ! 1=32 is a constant. We show that if n is sufficiently large then there is a Hamiltonian cycle in which each edge is a different colour, thereby proving a 1986 conjecture of Hahn and Thomass ..."
Abstract - Cited by 35 (8 self) - Add to MetaCart
The edges of the complete graph K n are coloured so that no colour appears more than dcne times, where c ! 1=32 is a constant. We show that if n is sufficiently large then there is a Hamiltonian cycle in which each edge is a different colour, thereby proving a 1986 conjecture of Hahn

EDGE-DISJOINT HAMILTON CYCLES IN GRAPHS

by Demetres Christofides, Daniela Kühn, Deryk Osthus , 2009
"... In this paper we give an approximate answer to a question of Nash-Williams from 1970: we show that for every α> 0, every sufficiently large graph on n vertices with minimum degree at least (1/2 + α)n contains at least n/8 edge-disjoint Hamilton cycles. More generally, we give an asymptotically b ..."
Abstract - Cited by 10 (6 self) - Add to MetaCart
In this paper we give an approximate answer to a question of Nash-Williams from 1970: we show that for every α> 0, every sufficiently large graph on n vertices with minimum degree at least (1/2 + α)n contains at least n/8 edge-disjoint Hamilton cycles. More generally, we give an asymptotically

Enumeration of Basic Hamilton Cycles in the Mangoldt

by Levaku Madhavi, Tekuri Chalapati
"... The Mangoldt graph Mn is an arithmetic function, namely, Mangoldt function (n), n ≥ 1 an integer. In this paper the notion of a basic Hamilton cycles in Mn is introduced and their number is enumerated. ..."
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The Mangoldt graph Mn is an arithmetic function, namely, Mangoldt function (n), n ≥ 1 an integer. In this paper the notion of a basic Hamilton cycles in Mn is introduced and their number is enumerated.
Results 1 - 10 of 83,198