Abstract
In Gao’s previous work, the authors determined several degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if b = f(x) = g(x) = a for all vertices x in G. In this paper, we continue to discuss these degree conditions for admitting fractional factor in the setting that several vertices and edges are removed and there is a difference Δ between g(x) and f(x) for every vertex x in G. These obtained new degree conditions reformulate Gao’s previous conclusions, and show how Δ acts in the results. Furthermore, counterexamples are structured to reveal the sharpness of degree conditions in the setting f(x) = g(x) + Δ.
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Supported by NSFC (Grant Nos. 11761083, 11771402 and 11671053), Fundación Séneca (Spain) (Grant No. 20783/PI/18) and Ministry of Science, Innovation and Universities (Spain) (Grant No. PGC2018-097198-B-100)
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Gao, W., Wang, W.F. & Guirao, J.L.G. The Extension Degree Conditions for Fractional Factor. Acta. Math. Sin.-English Ser. 36, 305–317 (2020). https://doi.org/10.1007/s10114-020-9156-0
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DOI: https://doi.org/10.1007/s10114-020-9156-0