Titlebook: Hamiltonian Cycle Problem and Markov Chains; Vivek S. Borkar,Vladimir Ejov,Giang T. Nguyen Book 2012 Springer Science+Business Media, LLC

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Determinants (3.14). The authors prove that for positive and sufficiently small values of ε, determining the Hamiltonicity of a given graph is equivalent to minimising the top-left element of the fundamental matrix . of an MDP associated with the given graph, over the space of feasible deterministic policies ..

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Tracestop-left elements of the fundamental matrices like in Chapter 3, or maximising the determinant of the inverse of the fundamental matrices like in Chapter 5, one can minimise the traces of the fundamental matrices to determine the Hamiltonicity of a given graph. While it is unclear whether the trace

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Linear Programming Based Algorithmscupational measures is a polyhedron with extreme points corresponding to all spanning subgraphs of the given graph. Furthermore, from Theorem 4.1 we learned that a simple cut of the above domain yields a polyhedron the extreme points of which correspond to only two possible types: Hamiltonian cycles

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Interior Point and Cross-Entropy Algorithmsthe Hamiltonian cycle problem: the . and the .. In particular, the first algorithm searches in the interior of the convex domain of doubly stochastic matrices induced by a given graph, with the goal of converging to an extreme point corresponding to a permutation matrix that coincides with a Hamilto

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Self-similar Structure and Hamiltonicityomplete for this class and because there is freely available, reliable, software for enumerating all connected cubic graphs with N vertices (see, for example, Meringer [77]). This offers an opportunity to study the whole populations of these graphs with the goal of understanding the special nature o

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Graph Enumerationt introduction to the topic of graph enumeration. On counting labeled cubic graphs, there has been a series of results, most notably Read [86], Read [87], Wormald [101], and Wormald [102], which collectively present various approaches for counting labeled cubic graphs, and labeled cubic graphs with

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978-1-4899-9227-7Springer Science+Business Media, LLC 2012

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Hamiltonian Cycle Problem and Markov Chains978-1-4614-3232-6Series ISSN 0884-8289 Series E-ISSN 2214-7934

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https://doi.org/10.1007/978-1-4614-3232-6Combinatorial Optimization; Graphing; Hamiltonian Cycle Problem; Markov Chains; Mathematical Programming

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https://doi.org/10.1007/978-3-030-90602-3In this book, all graphs are connected and undirected, unless otherwise stated. We follow the graph terminology and conventions from Harary [57], where the reader can find an excellent introduction to graph theory. Consider a graph . = (. (.);.(.)) = (., .), where . is the set of vertices of ., |V| = ., and . is the set of edges on ..