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Hamiltonian Paths (hamiltonian + paths)
Selected AbstractsMetamaterial inclusions based on grid-graph Hamiltonian pathsMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 12 2006Vincenzo Pierro Abstract This article deals with a study of novel classes of metamaterial inclusions based on space-filling curves. The graph,theoretic Hamiltonian-path (HP) concept is exploited to construct a fairly broad class of space-filling curve geometries that include as special cases the well-known Hilbert an Peano curves whose application to metamaterial inclusions has recently been proposed. In this framework, the basic properties of HP are briefly reviewed, and a full-wave study of the electromagnetic properties of representative grid-graph HP geometries is carried out. Applications to metamaterial inclusions are explored, with focus on artificial magnetic conductors with reduced polarization-sensitivity. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48:2520,2524, 2006; Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.21982 [source] On the maximum number of Hamiltonian paths in tournamentsRANDOM STRUCTURES AND ALGORITHMS, Issue 3 2001Ilan Adler By using the probabilistic method, we show that the maximum number of directed Hamiltonian paths in a complete directed graph with n vertices is at least (e,o(1)) (n!/2n,1). © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 291,296, 2001 [source] Hamiltonian cycles and paths with a prescribed set of edges in hypercubes and dense setsJOURNAL OF GRAPH THEORY, Issue 2 2006Rostislav Caha Abstract This paper studies techniques of finding hamiltonian paths and cycles in hypercubes and dense sets of hypercubes. This problem is, in general, easily solvable but here the problem was modified by the requirement that a set of edges has to be used in such path or cycle. The main result of this paper says that for a given n, any sufficiently large hypercube contains a hamiltonian path or cycle with prescribed n edges just when the family of the edges satisfies certain natural necessary conditions. Analogous results are presented for dense sets. © 2005 Wiley Periodicals, Inc. J Graph Theory [source] Mutually independent hamiltonian paths in star networksNETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2005Cheng-Kuan Lin Abstract Two hamiltonian paths P1 = ,u1, u2,,,un(G), and P2 = ,v1, v2,,,vn(G), of G from u to v are independent if u = u1 = v1, v = vn(G) = un(G), and vi , ui for every 1 < i < n(G). A set of hamiltonian paths, {P1, P2,,,Pk}, of G from u to v are mutually independent if any two different hamiltonian paths are independent from u to v. A bipartite graph G is hamiltonian laceable if there exists a hamiltonian path joining any two nodes from different partite sets. A bipartite graph is k -mutually independent hamiltonian laceable if there exists k -mutually independent hamiltonian paths between any two nodes from distinct partite sets. The mutually independent hamiltonian laceability of a bipartite graph G, IHPL(G), is the maximum integer k such that G is k -mutually independent hamiltonian laceable. Let Sn denote the n -dimensional star graph. We prove that IHPL(S2) = 1, IHPL(S3) = 0, and IHPL(Sn) = n, 2 if n , 4. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(2), 110,117 2005 [source] | ||||||||||