Abstract
Some structures of spanning trees with many or less leaves in a connected graph are determined. We show (1) a connected graph G has a spanning tree T with minimum leaves such that T contains a longest path, and (2) a connected graph G on n vertices contains a spanning tree T with the maximum leaves such that Δ(G) = Δ(T) and the number of leaves of T is not greater than n − D(G) + 1, where D(G) is the diameter of G.
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Supported by the National Natural Science Foundation of China (No. 10771091) and Project of Knowledge and Science Innovation Program of Northwest Normal University (Grant No. NWNU-KJCXGC-3-47).
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Yao, B., Zhang, Zf. & Wang, Jf. Some results on spanning trees. Acta Math. Appl. Sin. Engl. Ser. 26, 607–616 (2010). https://doi.org/10.1007/s10255-010-0011-4
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DOI: https://doi.org/10.1007/s10255-010-0011-4