13 papers
Minimal Cayley graphs with large chromatic number
James Davies, Meike Hatzel, Liana Yepremyan
Resolving Babai's minimal Cayley graph problem, we construct finite minimal Cayley graphs with arbitrarily large chromatic number.
Rational exponents near 3/2
Tao Jiang, Sean Longbrake, Liana Yepremyan
Given a graph , the extremal number is the maximum number of edges in an -vertex graph not containing as a subgraph. The well-known rational exponents conjectur…
On the generalized Turán number of complete bipartite graphs
Oliver Janzer, Sean Longbrake, Liana Yepremyan
For graphs and , the generalized Turán number denotes the maximum number of copies of in an -free graph on vertices. We prove that if $s\in…
On the number of families avoiding a subposet
Tao Jiang, Sean Longbrake, Liana Yepremyan
In this paper we show that for any poset that is not an antichain, the number of induced -free families in the Boolean lattice is at most $ 2^{O(\mathrm{La}^*(n,P)…
Towards Graham's rearrangement conjecture via rainbow paths
Matija BuciÄ, Bryce Frederickson, Alp Müyesser +2
We study an old question in combinatorial group theory which can be traced back to a conjecture of Graham from 1971. Given a group , and some subset , is it poss…
Long cycles in vertex transitive digraphs
Matija BuciÄ, Kevin Hendrey, Bojan Mohar +2
One of the most well-known conjectures concerning Hamiltonicity in graphs asserts that any sufficiently large connected vertex transitive graph contains a Hamilton cycle. In this f…