Abstract
Let G be a graph of order n. The binding number \(\text{ bind }(G)\) of G is \(\min \{\frac{|N_{G}(X)|}{|X|}\mid \emptyset \ne X\subseteq V(G)\,\, \text{ and }\,\, N_{G}(X)\ne V(G)\}\). Throughout this article, some sufficient conditions about neighborhood union and \(\text{ bind }(G)\) for a graph G to be fractional covered are obtained. Moreover, some graphs to verify that the results are best possible in a certain sense are gotten.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 11731002), the Fundamental Research Funds for the Central Universities (Nos. 2016JBZ012, 2016JBM071) and the 111 Project of China (B16002).
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Communicated by Xueliang Li.
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Yuan, Y., Hao, RX. Neighborhood union conditions for fractional [a, b]-covered graphs. Bull. Malays. Math. Sci. Soc. 43, 157–167 (2020). https://doi.org/10.1007/s40840-018-0669-y
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DOI: https://doi.org/10.1007/s40840-018-0669-y