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    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/66389

    Title: 20-Relative Neighborhood Graphs Are Hamiltonian
    Authors: M. S. Chang;C. Y. Tang;R. C. T. Lee
    教師: 唐傳義
    Date: 1991
    Publisher: John Wiley & Sons
    Relation: Journal of Graph Theory,Volume 15,Issue 5,November 1991,Pages 543 - 557
    Keywords: Hamiltonian
    Relative Neighborhood Graph
    Abstract: For any two points p and q in the Euclidean plane, define LUNpq = {v|v R2, dpv < dpq and dqv < dpq}, where duv is the Euclidean distance between two points u and v. Given a set of points V in the plane, let LUNpq(V) = V LUNpq. Toussaint defined the relative neighborhood graph of V, denoted by RNG(V) or simply RNG, to be the undirected graph with vertices V such that for each pair p,q V, (p,q) is an edge of RNG(V) if and only if LUNpq (V) = . The relative neighborhood graph has several applications in pattern recognition that have been studied by Toussaint. We shall generalize the idea of RNG to define the k-relative neighborhood graph of V, denoted by kRNG(V) or simply kRNG, to be the undirected graph with vertices V such that for each pair p,q V, (p,q) is an edge of kRNG(V) if and only if | LUNpq(V) | < k, for some fixed positive number k. It can be shown that the number of edges of a kRNG is less than O(kn). Also, a kRNG can be constructed in O(kn2) time. Let Ec = {epq| p V and q V}. Then Gc = (V,Ec) is a complete graph. For any subset F of Ec, define the maximum distance of F as maxepqFdpq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph Gc whose maximum distance is the minimum among all Hamiltonian cycles in graph Gc. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian.
    URI: http://www.wiley.com/
    Appears in Collections:[資訊工程學系] 期刊論文

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