科研之友
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摘要
For a positive integer k, a graph G is k-ordered hamiltonian if for every ordered sequence of k vertices there is a hamiltonian cycle that encounters the vertices of the sequence in the given order. In this paper, we show that if G is a left perpendicular3k/2right perpendicular-connected graph of order n <= 100k, and d(u) + d(v) >= n for any two vertices u and v with d(u, v) = 2, then G is k-ordered hamiltonian. Our result implies the theorem of G. Chen et al. [Ars Combin. 70 (2004) 245-255) [1], which requires the degree sum condition for all pairs of non-adjacent vertices, not just those distance 2 apart.
- 出版日期2010-7-31
- 单位山西大学
