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Spanning trees with many leaves. (English) Zbl 0986.05030
In this paper, it is shown that for every $$t\geq 2$$, and every graph $$G=(V,E)$$ with $$|V|\neq t+2$$ and $$|E|\geq |V|+ t(t-1)/2$$, $$G$$ has a spanning tree with more than $$t$$ leaves. This bound is sharp. Similar results are given for the case that $$|V|=t+2$$.

##### MSC:
 05C05 Trees
##### Keywords:
spanning tree; leaves
Full Text:
##### References:
 [1] Griggs, Discrete Math 104 pp 167– (1992) · Zbl 0776.05031 [2] and Spanning trees with many leaves, lecture at SIAM Discrete Math, Conf., San Francisco, 1988. [3] The maximum leaf spanning tree problem for cubic graphs is NP-complete, Institute for Mathematics and its Application, preprint, 1998. [4] Storer, Inform Process Lett 13 pp 8– (1981) · Zbl 0482.05031
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