Name
Abstract | ||
|---|---|---|
Let uk(G,p) be the maximum over all k-vertex graphs F of by how much the number of induced copies of F in G differs from its expectation in the binomial random graph with the same number of vertices as G
and with edge probability p. This may be viewed as a measure of how close G is to being p-quasirandom. For a positive integer n and 0<p<1, let D(n,p) be the distance from pn2 to the nearest integer. Our main result is that, for fixed k≥4 and for n large, the minimum of uk(G,p) over n-vertex graphs has order of magnitude Θ(max{D(n,p),p(1−p)}nk−2) provided that p(1−p)n1∕2→∞. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.ejc.2018.05.007 | European Journal of Combinatorics |
Field | DocType | Volume |
Integer,Discrete mathematics,Graph,Nearest integer function,Combinatorics,Random graph,Vertex (geometry),Binomial,Order of magnitude,Mathematics | Journal | 73 |
ISSN | Citations | PageRank |
0195-6698 | 0 | 0.34 |
References | Authors | |
4 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Humberto Naves | 1 | 24 | 4.08 |
| Oleg Pikhurko | 2 | 318 | 47.03 |
| Alex Scott | 3 | 251 | 40.93 |