Publication details
MORE NON-BIPARTITE FORCING PAIRS
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Acta Mathematica Universitatis Comenianae |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1279 |
| Keywords | Quasirandom graphs; Forcing Conjecture |
| Description | We study pairs of graphs (H-1, H-2) such that every graph with the densities of H-1 and H-2 close to the densities of H-1 and H-2 in a random graph is quasirandom; such pairs (H-1, H-2) are called forcing. Non-bipartite forcing pairs were first discovered by Conlon, Han, Person and Schacht [Weak quasi-randomness for uniform hypergraphs, Random Structures Algorithms 40 (2012), no. 1, 1-38]: they showed that (K-t, F) is forcing where F is the graph that arises from K-t by iteratively doubling its vertices and edges in a prescribed way t times. Reiher and Schacht [Forcing quasirandomness with triangles, Forum of Mathematics, Sigma. Vol. 7, 2019] strengthened this result for t = 3 by proving that two doublings suffice and asked for the minimum number of doublings needed for t > 3. We show that [t + 1)/2] doublings always suffice. |