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 Title: Caterpillar Factorizations of Crowns Authors: Lee,HC;Lee,MJ;Lin,C Contributors: 數學系 Keywords: COMPLETE BIPARTITE GRAPHS;COMPLETE MULTIPARTITE GRAPHS;PATH FACTORIZATIONS;STAR-FACTORIZATIONS;DIGRAPHS;DESIGNS 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. Relation: ARS COMBINATORIA Appears in Collections: [數學系] 期刊論文

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