Note on Sparse Random Graphs and Cover Graphs

It is shown in this note that with high probability it is enough to destroy all triangles in order to get a cover graph from a random graph Gn,p with p log n/n for any constant < 2/3. On the other hand, this is not true for somewhat higher densities: If p (log n)3/(n log log n) with > 1/8 then with high probability we need to delete more edges than one from every triangle. Our result has a natural algorithmic interpretation.

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Tom Bohman, Alan M. Frieze, Miklós Ruszinkó, Lubos Thoma
• Keywords: COMBINATORICS 2000, Cover Graph, Random Graph, Triangle