论文标题
关于超图的公平可着色性缺陷
Regarding Equitable Colorability Defect of Hypergraphs
论文作者
论文摘要
\ \ noindent azarpendar和Jafari在2020年证明了以下不等式$$χ\ weft（{\ rm kg} ^r（{\ cal f}，s）\ right）\ geq \ geq \ geq \ geq \ left \ left \ lest \ lest \ left \ frac {{\ rm ecd} {\ rm ecd} \ frac {s} {2} \ right \ rfloor \ right）}} {r-1} \ right \ rceil，$$，并指出，如果一个替换$ \ \ left \ left \ left \ lfloor \ lfloor \ frac {s} {s} {2} {2} {2} {2} {2} {2} \ rfror $ s $ $ s $ $ s $ $ s. \在本文中，考虑了关系$ {\ rm ecd}^r \ left（{\ cal f}，x \ right）\ geq {\ rm cd}^r \ left（{\ cal f}，{\ cal f}，x \ right）$，我们总是表明，我们在弱小的nme equ $ equ $ neque中（\ qu） （{\ cal f}，s）\ right）\ geq \ left \ lceil \ frac {{\ rm cd}^r \ left（{\ cal f}，\ left \ left \ lfloor \ lfloor \ frac {s}大于$ \ left \ lfloor \ frac {s} {2} {2} \ right \ rfloor $可以用$ \ left \ lfloor \ lfloor \ frac {s} {2} {2} \ right \ rfloor $代替。
\noindent Azarpendar and Jafari in 2020 proved the following inequality $$χ\left( {\rm KG} ^r ({\cal F} , s) \right) \geq \left\lceil \frac{ {\rm ecd}^r \left( {\cal F} , \left\lfloor \frac{s}{2} \right\rfloor \right) }{r-1} \right\rceil ,$$ and noted that it is plausible that the above inequality remains true if one replaces $\left\lfloor \frac{s}{2} \right\rfloor$ with $s$. \noindent In this paper, considering the relation ${\rm ecd}^r \left( {\cal F} , x \right) \geq {\rm cd}^r \left( {\cal F} , x \right)$ which always holds, we show that even in the weaker inequality $$χ\left( {\rm KG} ^r ({\cal F} , s) \right) \geq \left\lceil \frac{ {\rm cd}^r \left( {\cal F} , \left\lfloor \frac{s}{2} \right\rfloor \right) }{r-1} \right\rceil ,$$ no number $x$ greater than $\left\lfloor \frac{s}{2} \right\rfloor$ could be replaced by $\left\lfloor \frac{s}{2} \right\rfloor$.
