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Connectivity and dynamics for random subgraphs of the directed cube

✍ Scribed by Béla Bollobás; Craig Gotsman; Eli Shamir

Book ID
112892151
Publisher
The Hebrew University Magnes Press
Year
1993
Tongue
English
Weight
323 KB
Volume
83
Category
Article
ISSN
0021-2172

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Erdős has conjectured that every subgraph of the n-cube Q n having more than (1/2+o(1))e(Q n ) edges will contain a 4-cycle. In this note we consider 'layer' graphs, namely, subgraphs of the cube spanned by the subsets of sizes k -1, k and k + 1, where we are thinking of the vertices of Q n as being