Binding Numbers and Connected Factors |
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Authors: | Yunsun Nam |
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Affiliation: | (1) College of Chemistry, Chemical Engineering and Materials Science, Shandong Normal University, Jinan, 250014, China;(2) College of Pharmacy, Shandong University of Traditional Chinese Medicine, Jinan, 250014, China; |
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Abstract: | In this paper, we obtain some sufficient conditions based on binding number for a graph to have a connected factor with degree restrictions. Let α and k be positive integers with α + k ≥ 4. Let G be a connected graph with a spanning subgraph F, each component of which has order at least α. We show that if the binding number of G is greater than (α k − α)/(α k − α −1) (k ≥ 2) and α/(α −2) (k = 1) then G has a connected subgraph which has F and in which every vertex v has degree at most deg F (v) + k. From the result, we derive various sufficient conditions for a graph to have a connected [a, b]-factor. |
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