Abstract
Let G be a connected graph, let \({X \subset V(G)}\) and let f be a mapping from X to {2, 3, . . .}. Kaneko and Yoshimoto (Inf Process Lett 73:163–165, 2000) conjectured that if |N G (S) − X| ≥ f (S) − 2|S| + ω G (S) + 1 for any subset \({S \subset X}\), then there exists a spanning tree T such that d T (x) ≥ f (x) for all \({x \in X}\). In this paper, we show a result with a stronger assumption than this conjecture; if |N G (S) − X| ≥ f (S) − 2|S| + α(S) + 1 for any subset \({S \subset X}\), then there exists a spanning tree T such that d T (x) ≥ f (x) for all \({x \in X}\).
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Kaneko A., Yoshimoto K.: On spanning trees with restricted degrees. Inf. Process. Lett. 73, 163–165 (2000)
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Ozeki, K., Yamashita, T. A Spanning Tree with High Degree Vertices. Graphs and Combinatorics 26, 591–596 (2010). https://doi.org/10.1007/s00373-010-0933-x
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DOI: https://doi.org/10.1007/s00373-010-0933-x