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83,198
Tournaments with many Hamilton cycles
"... The object of interest is the maximum number, h(n), of Hamilton cycles in an ntournament. 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 ..."
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Cited by 6 (0 self)
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The object of interest is the maximum number, h(n), of Hamilton cycles in an ntournament. 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
, 2015
"... We show that, for a natural notion of quasirandomness in kuniform hypergraphs, any quasirandom kuniform 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 kuniform hypergraph satisfying ..."
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We show that, for a natural notion of quasirandomness in kuniform hypergraphs, any quasirandom kuniform 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 kuniform hypergraph satisfying
Voltage Graphs and Hamilton Cycles
, 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
, 2008
"... We prove that any kuniform 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 3uniform case. Though some additional difficulties arise in the kuniform case, our argument her ..."
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Cited by 5 (1 self)
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We prove that any kuniform 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 3uniform case. Though some additional difficulties arise in the kuniform case, our argument
Hamilton Cycles in the Union of Random Permutations
, 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. ..."
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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
, 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 ..."
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Cited by 1 (0 self)
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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
, 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. ..."
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Cited by 5 (2 self)
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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
 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 ..."
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Cited by 35 (8 self)
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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
EDGEDISJOINT HAMILTON CYCLES IN GRAPHS
, 2009
"... In this paper we give an approximate answer to a question of NashWilliams 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 edgedisjoint Hamilton cycles. More generally, we give an asymptotically b ..."
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Cited by 10 (6 self)
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In this paper we give an approximate answer to a question of NashWilliams 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 edgedisjoint Hamilton cycles. More generally, we give an asymptotically
Enumeration of Basic Hamilton Cycles in the Mangoldt
"... 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
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83,198