zbMATH — the first resource for mathematics

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 \(|V|=t+2\).

05C05 Trees
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.