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摘要
As usual, K-m,K-n, denotes the complete bipartite graph with parts of sizes m and n. For positive integers k %26lt;= n, the crown C-n,C-k is the graph with vertex set {a(0), a(1), ..., a(n-1), b(0), b(1), ..., b(n-1)} and edge set {a(i)b(j): 0 %26lt;= i %26lt;= n - 1, j = i, i + 1, ..., i + k - 1 (mod n)}. A spider is a tree with at most one vertex of degree more than two, called the center of the spider. A leg of a spider is a path from the center to a vertex of degree one. Let S-l(t) denote a spider of l legs, each of length t. An H-decomposition of a graph G is an edge-disjoint decomposition of G into copies of H. In this paper we investigate the problems of S-l(2)-decompositions of complete bipartite graphs and crowns, and prove that: (1) K-n,K-tl has an S-l(2)-decomposition if and only if nt equivalent to 0 (mod 2), n %26gt;= 2l if t = 1, and n %26gt;= l if t %26gt;= 2, (2) for t %26gt;= 2 and n %26gt;= tl, has an S-l(2)-decomposition if and only if nt equivalent to 0 (mod 2), (3) for n %26gt;= 3t, C-n,C-3t has an S-3(2)-decomposition if and only if nt equivalent to 0 (mod 2) and n equivalent to 0 (mod 4) if t = 1.
- 出版日期2013-10
- 单位中央民族大学
