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Applied Mathematics and Computation, 1992
We present some conditions equivalent to the existence of a Hamiltonian cycle in a graph on n vertices. Among other things, we show that for each n, there is an explicitly determined nxn diagonal matrix D such that if A is the adjacency matrix of such a graph, then the existence of a Hamiltonian cycle is completely determined by the eigenvalues of AD ...
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We present some conditions equivalent to the existence of a Hamiltonian cycle in a graph on n vertices. Among other things, we show that for each n, there is an explicitly determined nxn diagonal matrix D such that if A is the adjacency matrix of such a graph, then the existence of a Hamiltonian cycle is completely determined by the eigenvalues of AD ...
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Hamiltonian Cycles and Markov Chains
Mathematics of Operations Research, 1994In this paper we derive new characterizations of the Hamiltonian cycles of a directed graph, and a new LP-relaxation of the Traveling Salesman Problem. Our results are obtained via an embedding of these combinatorial optimization problems in suitably perturbed controlled Markov chains.
Filar, JA, Krass, D
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Distributing vertices on Hamiltonian cycles
Journal of Graph Theory, 2011AbstractLet G be a graph of order n and 3≤t≤n/4 be an integer. Recently, Kaneko and Yoshimoto [J Combin Theory Ser B 81(1) (2001), 100–109] provided a sharp δ(G) condition such that for any set X of t vertices, G contains a hamiltonian cycle H so that the distance along H between any two vertices of X is at least n/2t.
Faudree, Ralph J.+3 more
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THE COMPLEXITY OF THOMASON’S ALGORITHM FOR FINDING A SECOND HAMILTONIAN CYCLE
Bulletin of the Australian Mathematical Society, 2018Liang Zhong
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State preparation and evolution in quantum computing: A perspective from Hamiltonian moments
International Journal of Quantum Chemistry, 2022Trevor Keen, Bo Peng
exaly
On the Exact Complexity of Hamiltonian Cycle and q-Colouring in Disk Graphs
International/Italian Conference on Algorithms and Complexity, 2017Sándor Kisfaludi-Bak+1 more
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Annals of the New York Academy of Sciences, 1989
Feng Tian, Zhenhong Liu, Yongjin Zhu
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Feng Tian, Zhenhong Liu, Yongjin Zhu
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Hamiltonian Cycle and Path Embeddings in 3-Ary n-Cubes Based on K1,2-Structure Faults
2016 IEEE Trustcom/BigDataSE/ISPA, 2016Yali Lv, Cheng-Kuan Lin, Jianxi Fan
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Hamiltonian-Driven Adaptive Dynamic Programming With Approximation Errors
IEEE Transactions on Cybernetics, 2022Chengzhong Xu+2 more
exaly