六角图的改进的近似多色性
Improved approximative multicoloring of hexagonal graphs
摘要：
1999年，McDiarmid和Reed证明了对于一般的加权六角图，多色数对加权团数的逼近比$9/8$是渐近的最佳可能.我们证明，有一个适当的多色的$G$，使用最多$15 \lfloor\frac{ω(G)}{12}\rfloor+ 18 $的颜色，提高最好的以前已知的asimptotic比从4/3到5/4。
英文摘要：
In 1999, McDiarmid and Reed conjectued that the approximation ratio $9/8$ of multichromatic number to weighted clique number asymptotically is the best possible for general weighted hexagonal graphs. We prove that there is a proper multicoloring of $G$ that uses at most $15 \lfloor\frac{ω(G)}{12}\rfloor+ 18 $ colors improving the best previously known asimptotic ratio from 4/3 to 5/4.
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。
