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Hedetniemi's conjecture is asymptotically false
Journal of Combinatorial Theory Series B ( IF 1.4 ) Pub Date : 2020-03-13 , DOI: 10.1016/j.jctb.2020.03.003
Xiaoyu He , Yuval Wigderson

Extending a recent breakthrough of Shitov, we prove that the chromatic number of the tensor product of two graphs can be a constant factor smaller than the minimum chromatic number of the two graphs. More precisely, we prove that there exists an absolute constant δ>0 such that for all c sufficiently large, there exist graphs G and H with chromatic number at least (1+δ)c for which χ(G×H)c.



中文翻译:

赫德涅米的猜想在渐近上是错误的

扩展了Shitov的最新突破,我们证明了两个图的张量积的色数可以是小于两个图的最小色数的常数因子。更确切地说,我们证明存在一个绝对常数δ>0这样对于所有足够大的c,存在色数至少为G的HH1个+δC 为此 χG×HC

更新日期:2020-04-21
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