Abstract
Win proved a well-known result that the graph G of connectivity κ(G) with α(G) ≤ κ(G) + k − 1 (k ≥ 2) has a spanning k-ended tree, i.e., a spanning tree with at most k leaves. In this paper, the authors extended the Win theorem in case when κ(G) = 1 to the following: Let G be a simple connected graph of order large enough such that α(G) ≤ k + 1 (k ≥ 3) and such that the number of maximum independent sets of cardinality k + 1 is at most n − 2k − 2. Then G has a spanning k-ended tree.
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This work was supported by the National Natural Science Foundation of China (Nos. 11871099, 11671037, 11801296) and the Nature Science Foundation from Qinghai Province (No. 2017-ZJ-949Q).
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Lei, W., Xiong, L., Du, J. et al. An Extension of the Win Theorem: Counting the Number of Maximum Independent Sets. Chin. Ann. Math. Ser. B 40, 411–428 (2019). https://doi.org/10.1007/s11401-019-0141-9
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DOI: https://doi.org/10.1007/s11401-019-0141-9