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Chromatic Numbers of Distance Graphs with Several Forbidden Distances and without Cliques of a Given Size
Problems of Information Transmission ( IF 0.5 ) Pub Date : 2018-04-13 , DOI: 10.1134/s0032946018010064 A. V. Berdnikov
Problems of Information Transmission ( IF 0.5 ) Pub Date : 2018-04-13 , DOI: 10.1134/s0032946018010064 A. V. Berdnikov
We consider distance graphs with k forbidden distances in an n-dimensional space with the p-norm that do not contain cliques of a fixed size. Using a probabilistic construction, we present graphs of this kind with chromatic number at least (Bk)Cn, where B and C are constants.
中文翻译:
具有多个禁止距离且没有给定大小的派系的距离图的色数
我们考虑在n维空间中具有p个范数的k个禁止距离的距离图,其中不包含固定大小的派系。使用概率构造,我们呈现这种色数至少为(Bk)Cn的图,其中B和C为常数。
更新日期:2018-04-13
中文翻译:
具有多个禁止距离且没有给定大小的派系的距离图的色数
我们考虑在n维空间中具有p个范数的k个禁止距离的距离图,其中不包含固定大小的派系。使用概率构造,我们呈现这种色数至少为(Bk)Cn的图,其中B和C为常数。