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    NCU Institutional Repository > 理學院 > 數學系 > 期刊論文 >  Item 987654321/51126

    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51126

    Title: Caterpillar Factorizations of Crowns
    Authors: Lee,HC;Lee,MJ;Lin,C
    Contributors: 數學系
    Date: 2010
    Issue Date: 2012-03-27 18:22:30 (UTC+8)
    Publisher: 國立中央大學
    Abstract: For positive integers k <= n, the crown C(n,k) is the graph with vertex set {a(0), a(1),..., a(n-1), b(0), b(1),..., b(n-i)} and edge set {a(i)b(j) : 0 <= i <= 1, j = i + 1, i + 2,..., i + k ( mod n)}. A caterpillar is a tree of order at least three which contains a path such that each vertex not on the path is adjacent to a vertex on the path. Being a connected bipartite graph, a caterpillar is balanced if the two parts of the bipartition of its vertices have equal size; otherwise, it is unbalanced. In this paper we obtain the necessary and sufficient condition for balanced-caterpillar factorization of crowns. The Criterion for unbalanced-caterpillar factorization of crowns is open. We also obtain the necessary and sufficient condition for directed caterpillar factorization of symmetric crowns.
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