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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
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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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