Abstract
In this paper, we prove that an m-connected graph G on n vertices has a spanning tree with at most k leaves (for k ≥ 2 and m ≥ 1) if every independent set of G with cardinality m + k contains at least one pair of vertices with degree sum at least n − k + 1. This is a common generalization of results due to Broersma and Tuinstra and to Win.
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Bondy, J.A.: Basic Graph Theory: Paths and Circuits, in: Handbook of Combinatorics, Vol. I, Graham, R., Grőtshel, M., and Lovász, L. (eds), Elsevier, Amsterdam 1995, pp. 5–110
Broersma, H., Tuinstra, H.: Independence trees and Hamilton cycles. J. Graph Theory 29, 227–237 (1998)
Chvátal, V., Erdős, P.: A note on hamiltonian circuits, Discrete Math. 2, 111–113 (1972)
Ore, O.: Note on Hamilton circuits, Am. Math. Monthly 67, 55 (1960)
Win, S.: On a conjecture of Las Vergnas concerning certain spanning trees in graphs, Resultate Math. 2, 215–224 (1979)
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Tsugaki, M., Yamashita, T. Spanning Trees with Few Leaves. Graphs and Combinatorics 23, 585–598 (2007). https://doi.org/10.1007/s00373-007-0751-y
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DOI: https://doi.org/10.1007/s00373-007-0751-y