Interpolation theorem for the number of end‐vertices of spanning trees

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Abstract
The following interpolation theorem is proved: If a graph G contains spanning trees having exactly m and n end‐vertices, with m < n, then for every integer k, m < k < n, G contains a spanning tree having exactly k end‐vertices. This settles a problem posed by Chartrand at the Fourth International Conference on Graph Theory and Applications held in Kalamazoo, 1980.

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