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    National Tsing Hua University Institutional Repository > 歷任校長 > 李家同 (1993-1994) > 期刊論文  >  20-Relative Neighborhood Graphs Are Hamiltonian

    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/80791

    Title: 20-Relative Neighborhood Graphs Are Hamiltonian
    Authors: Chang, M. S.;Tang, C. Y.;Lee, R. C. T.
    教師: 李家同
    Date: 1991
    Publisher: Wiley-Blackwell
    Relation: JOURNAL OF GRAPH THEORY, Wiley-Blackwell, Volume 15, Issue 5, NOV 1991, Pages 543-557
    Keywords: Hamiltonian
    Abstract: For any two points p and q in the Euclidean plane, define LUN(pq) = {upsilon\upsilon) is-an-element-of R2, d(p-upsilon) < d(pq) and d(q-upsilon) < d(pq)}, where d(u-upsilon) is the Euclidean distance between two points u and upsilon. Given a set of points V in the plane, let LUN(pq)(V) = V or LUN(pq). 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 is-an-element-of V, (p,q) is an edge of RNG(V) if and only if LUN(pq)(V) = phi. 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 is-an-element-of V, (p,q) is an edge of kRNG(V) if and only if \LUN(pq)(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 E(c) = {e(pq\p is-an-element-of V and q is-an-element-of V}. Then G(c) = (V,E(c)) is a complete graph. For any subset F of E(c), define the maximum distance of F as max(e)pq is-an-element-of F)d(pq). A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph G(c) whose maximum distance is the minimum among all Hamiltonian cycles in graph G(c). We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian.
    Relation Link: http://as.wiley.com/WileyCDA/Brand/id-35.html
    URI: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/80791
    Appears in Collections:[李家同 (1993-1994)] 期刊論文
    [資訊工程學系] 期刊論文

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