Abstract
Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical (in short, fractional ID-k-factor-critical) if G - I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical, depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.
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This work is supported by the National Natural Science Foundation of China (Grant No. 11371009, 11501256, 61503160), Six Big Talent Peak of Jiangsu Province (Grant No. JY-022) and 333 Project of Jiangsu Province, the National Social Science Foundation of China (Grant No. 14AGL001), the Natural Science Foundation of Xinjiang Province of China (Grant No. 2015211A003) and the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No. 14KJD110002).
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Zhou, Sz., Xu, L. & Xu, Zr. Remarks on Fractional ID-k-factor-critical Graphs. Acta Math. Appl. Sin. Engl. Ser. 35, 458–464 (2019). https://doi.org/10.1007/s10255-019-0818-6
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DOI: https://doi.org/10.1007/s10255-019-0818-6