分数因子的扩张度条件
The Extension Degree Conditions for Fractional Factor
摘要：
在Gao的前期工作中，作者确定了在特定的条件下允许分数因子存在的图的几个图度条件。证明了如果对$G$中的所有顶点$x$都满足$b=f(x)=g(x)=a$，则这些度条件是紧的.本文继续讨论在去掉若干顶点和边，且对$G$中的每个顶点$x$，$g(x)$和$f(x)$之间存在一个$Δ$差的情况下，允许分数因子存在的度条件.这些新的度条件改写了Gao的结论，并说明了$Δ$在结果中的作用.此外，反例的结构，以揭示在设置$f(x)=g(x)+Δ$的程度条件的尖锐性。
英文摘要：
In Gao's previous work, the authors determined several graph 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 $f(x)=g(x)+Δ$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
