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Clique Numbers of Random Subgraphs of Some Distance Graphs
Problems of Information Transmission ( IF 0.5 ) Pub Date : 2018-07-14 , DOI: 10.1134/s0032946018020059
A. S. Gusev

We consider a class of graphs G(n, r, s) = (V (n, r),E(n, r, s)) defined as follows:$$V(n,r) = \{ x = ({x_{1,}},{x_2}...{x_n}):{x_i} \in \{ 0,1\} ,{x_{1,}} + {x_2} + ... + {x_n} = r\} ,E(n,r,s) = \{ \{ x,y\} :(x,y) = s\} $$where (x, y) is the Euclidean scalar product. We study random subgraphs G(G(n, r, s), p) with edges independently chosen from the set E(n, r, s) with probability p each. We find nontrivial lower and upper bounds on the clique number of such graphs.

中文翻译:

一些距离图的随机子图的集团数

我们考虑一类图Gn,r,s)=(Vnr),En,r,s))定义如下:$$ V(n,r)= \ {x =( {x_ {1,}},{x_2} ... {x_n}):{x_i} \ in \ {0,1 \},{x_ {1,}} + {x_2} + ... + {x_n } = r \},E(n,r,s)= \ {\ {x,y \}:(x,y)= s \} $$其中(xy)是欧几里德标量积。我们研究随机子图GGGnrs),p),其边独立从集合Enrs),每个概率为p。我们在此类图的集团数上找到了平凡的上下限。
更新日期:2018-07-14
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