科研之友
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摘要
Let G be a connected graph, let X subset of V (G) and let f be a mapping from X to {2, 3, ...}. Kaneko and Yoshimoto (Inf Process Lett 73: 163-165, 2000) conjectured that if vertical bar N(G) (S) - X vertical bar >= f (S) - 2 vertical bar S vertical bar + omega(G)(S) + 1 for any subset S subset of X, then there exists a spanning tree T such that d(T) (x) >= f (x) for all x is an element of X. In this paper, we show a result with a stronger assumption than this conjecture; if vertical bar N(G)(S) - X vertical bar >= f (S) - 2 vertical bar S vertical bar + alpha (S) + 1 for any subset S subset of X, then there exists a spanning tree T such that d(T) (x) >= f (x) for all x is an element of X.
- 出版日期2010-7
