arXiv subjects

Tamas Hubai

Publications and source records attributed to Tamas Hubai.

3 recordsLinked to original sources

arXiv2019

More non-bipartite forcing pairs

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), 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 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+2)/2 doublings always suffice.

math.CO↗

arXiv2017

Densities of 3-vertex graphs

Let d_i(G) be the density of the 3-vertex i-edge graph in a graph G, i.e., the probability that three random vertices induce a subgraph with i edges. Let S be the set of all quadruples (d_0,d_1,d_2,d_3) that are arbitrary close to 3-vertex graph densities in arbitrary large graphs. Huang, Linial, Naves, Peled and Sudakov have recently determined the projection of the set S to the (d_0,d_3) plane. We determine the projection of the set S to all the remaining planes.

math.CO↗

arXiv2016

Chromatic roots and limits of dense graphs

In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the chromatic polynomial extend to the theory of dense graph sequences. We offer a number of problems and conjectures motivated by this observation.

math.CO↗