科研之友
微信
新浪微博
Facebook
分享链接
摘要
We prove that the statement "for every infinite cardinal kappa, every graph with list-chromatic number. has coloring number at most (sci)(omega)(kappa)" proved by Kojman (2014) using the RGCH theorem implies the WRGCH theorem, which is a weaker relative of the RGCH, via a short forcing argument. Similarly, a better upper bound than (sci)(omega)(kappa) in this statement implies stronger (consistent) forms of the WRGCH theorem, the consistency of whose negations is wide open. Thus, the optimality of Kojman's upper bound is a purely cardinal arithmetic problem, and, as discussed below, is hard to decide.
- 出版日期2016-12
