11 papers
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…
Disjoint Paths in Expanders in Deterministic Almost-Linear Time via Hypergraph Perfect Matching
Matija BuciÄ, Zhongtian He, Shang-En Huang +1
We design efficient deterministic algorithms for finding short edge-disjoint paths in expanders. Specifically, given an -vertex -edge expander of conductance and min…
On Graham's rearrangement conjecture over
Benjamin Bedert, Matija BuciÄ, Noah Kravitz +2
A sequence of elements of a group is called a valid ordering if the partial products are all distinct. A long-standi…
The spanning tree spectrum: improved bounds and simple proofs
Noga Alon, Matija BuciÄ, Lior Gishboliner
The number of spanning trees of a graph , denoted , is a well studied graph parameter with numerous connections to other areas of mathematics. In a recent remarkable pape…
On a Ramsey--Turán variant of Roth's theorem
Matija BuciÄ, Micha Christoph, Jaehoon Kim +2
A classical theorem of Roth states that the maximum size of a solution-free set of a homogeneous linear equation in is if and only if the sum of…