Alp Müyesser

activity

20242026

collaborators

7 papers

math.CO2026

A proof of Andersen's rainbow path conjecture for large $n$

Candida Bowtell, Richard Montgomery, Alp Müyesser +1

We show that, for sufficiently large $n$ , every properly edge-coloured $n$ -vertex complete graph contains a path with $n - 1$ vertices which uses each colour at most once (that is, a…

math.CO2026

Robustness and hyperstability for the ErdÅs-Gallai theorem

Micha Christoph, Alp MÃ¼yesser, Yuval Wigderson

The ErdÅs--Gallai theorem states that every graph of average degree $d$ contains a cycle of length at least $d$ . We prove the following robust extension of the ErdÅs--Gallai theo…

math.CO2025

Cycle-factors of regular graphs via entropy

Micha Christoph, Nemanja DraganiÄ, AntÃ³nio GirÃ£o +3

It is a classical result that a random permutation of $n$ elements has, on average, about $lo g n$ cycles. We generalise this fact to all directed $d$ -regular graphs on $n$ vertice…

math.CO2025

Spanning spheres in Dirac hypergraphs

Freddie Illingworth, Richard Lang, Alp MÃ¼yesser +2

We show that a $k$ -uniform hypergraph on $n$ vertices has a spanning subgraph homeomorphic to the $(k - 1)$ -dimensional sphere provided that $H$ has no isolated vertices and each s…

math.CO2024

Random embeddings of bounded degree trees with optimal spread

A seminal result of KomlÃ³s, SÃ¡rkÃ¶zy, and SzemerÃ©di states that any n-vertex graph G with minimum degree at least (1/2 + Î±)n contains every n-vertex tree T of bounded degree. R…

math.CO2024

Optimal spread for spanning subgraphs of Dirac hypergraphs

Tom Kelly, Alp MÃ¼yesser, Alexey Pokrovskiy

Let $G$ and $H$ be hypergraphs on $n$ vertices, and suppose $H$ has large enough minimum degree to necessarily contain a copy of $G$ as a subgraph. We give a general method to rand…