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19,013
Hamiltonian Paths and Hyperbolic Patterns
"... In 1978 I thought it would be possible to design a computer algorithm to draw repeating hyperbolic patterns in a Poincaré disk based on Hamiltonian paths in their symmetry groups. The resulting successful program was capable of reproducing each of M.C. Escher’s four “Circle Limit ” patterns. The pro ..."
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In 1978 I thought it would be possible to design a computer algorithm to draw repeating hyperbolic patterns in a Poincaré disk based on Hamiltonian paths in their symmetry groups. The resulting successful program was capable of reproducing each of M.C. Escher’s four “Circle Limit ” patterns
Directed Hamiltonian Path
"... An algorithm for an NPcomplete problem is presented, namely the existence of a Directed Hamiltonian Path in a directed graph. The main advantage of this algorithm is that it uses exponentially less DNA than original approach of Adleman. It is an implementation of a classic result in a 1964 paper of ..."
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An algorithm for an NPcomplete problem is presented, namely the existence of a Directed Hamiltonian Path in a directed graph. The main advantage of this algorithm is that it uses exponentially less DNA than original approach of Adleman. It is an implementation of a classic result in a 1964 paper
Hamiltonian paths and cycles in hypertournaments
 J. GRAPH THEORY
, 1995
"... Given two integers n and k, n ≥ k> 1, a khypertournament T on n vertices is a pair (V, A), where V is a set of vertices, V  = n and A is a set of ktuples of vertices, called arcs, so that for any ksubset S of V, A contains exactly one of the k! ktuples whose entries belong to S. A 2hypert ..."
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Cited by 3 (1 self)
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’s) is Hamiltonian. T is strong if T has a path from x to y for every choice of distinct x, y ∈ V. We prove that every khypertournament on n (> k) vertices has a Hamiltonian path (an extension of Redei’s theorem on tournaments) and every strong khypertournament with n (> k + 1) vertices has a Hamiltonian
Hamiltonian paths in Cayley graphs
, 2008
"... The classical question raised by Lovász asks whether every Cayley graph is Hamiltonian. We present a short survey of various results in that direction and make some additional observations. In particular, we prove that every finite group G has a generating set of size at most log 2 G, such that th ..."
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Cited by 21 (0 self)
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The classical question raised by Lovász asks whether every Cayley graph is Hamiltonian. We present a short survey of various results in that direction and make some additional observations. In particular, we prove that every finite group G has a generating set of size at most log 2 G
Strong Tournaments with the Fewest Hamiltonian Paths
"... Busch recently determined the minimum number of Hamiltonian paths a strong tournament can have. We characterize the strong tournaments that realize this minimum. 1. ..."
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Busch recently determined the minimum number of Hamiltonian paths a strong tournament can have. We characterize the strong tournaments that realize this minimum. 1.
Long cycles in graphs without Hamiltonian paths
 Discrete Math
"... Long cycles in graphs without hamiltonian paths ..."
Powers of Hamiltonian Paths in Interval Graphs
 J. GRAPH THEORY
, 1998
"... We give a simple proof that the obvious necessary conditions for a graph to contain the k th power of a Hamiltonian path are sufficient for the class of interval graphs. The proof is based on showing that a greedy algorithm tests for the existence of Hamiltonian path powers in interval graphs. We ..."
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Cited by 8 (1 self)
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We give a simple proof that the obvious necessary conditions for a graph to contain the k th power of a Hamiltonian path are sufficient for the class of interval graphs. The proof is based on showing that a greedy algorithm tests for the existence of Hamiltonian path powers in interval graphs. We
Hamiltonian Paths In Projective Checkerboards
, 1998
"... Place a checker in some square of an n \Theta n checkerboard. The checker is allowed to step either to the east or to the north, and is allowed to step off the edge of the board in a manner suggested by the usual identification of the edges of the square to form a projective plane. We give an explic ..."
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Place a checker in some square of an n \Theta n checkerboard. The checker is allowed to step either to the east or to the north, and is allowed to step off the edge of the board in a manner suggested by the usual identification of the edges of the square to form a projective plane. We give an explicit description of all the routes that can be taken by the checker to visit each square exactly once.
Results 1  10
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