Geoffrey Simon was a student of Herbert von Karajan, Rudolf Kempe, Hans Swarowsky and Igor Markevich, and a major prize-winner at the first John Player International Conductors Award. 杰弗里‧西蒙是著名指挥家卡拉扬、甘比、史华洛夫斯基和马加域治的学生,也是第一届普列尔国际指挥大赛的主要得奖者。
Kempe refers that in the unavoidable structures group, a so-called simplifying problem cannot be solved which happens in the case of that a country or region has five neighboring countries or regions. 当年提出的“不可避免构形集”中一个国家(地域)具有五个邻国(邻域)的所谓“可约性”问题得不到解决。
This paper proves that counter example of Heawood is four-color by using Tait's methods, counter example of Tutte is also four-color by using Kempe's chains. 该文用Tait方法证明了Heawood反例是四色的;用Kempe链方法证明了Tutte反例也是四色的。
Kempe proved that this problem is NP-hard, and made a greedy algorithm, with better results. Kempe证明影响最大化是NP-hard,并提出了贪心算法,具有较好结果。