On the Turán number of the hypercube Page 1 Forum of Mathematics, Sigma (2024), Vol. 12:e38
1–19 doi:10.1017/fms.2024.27 RESEARCH ARTICLE On the Turán number of the hypercube …

We prove that every properly edge-colored n-vertex graph with average degree at least\(32
(\log 5n)^ 2\) contains a rainbow cycle, improving upon the\((\log n)^{2+ o (1)}\) bound due to …

In this survey we aim to give a comprehensive overview of results using sublinear
expanders. The term sublinear expanders refers to a variety of definitions of expanders …

In 1975, Erd\H {o} s asked for the maximum number of edges that an $ n $-vertex graph can
have if it does not contain two edge-disjoint cycles on the same vertex set. It is known that …

We prove that a binary linear code of block length $ n $ that is locally correctable with $3 $
queries against a fraction $\delta> 0$ of adversarial errors must have dimension at most …

Given a $ k $-uniform hypergraph $ H $ on $ n $ vertices, an even cover in $ H $ is a
collection of hyperedges that touch each vertex an even number of times. Even covers are a …

We prove that for every odd $ q\geq 3$, any $ q $-query binary, possibly non-linear locally
decodable code ($ q $-LDC) $ E:\{\pm1\}^ k\rightarrow\{\pm1\}^ n $ must satisfy $ k\leq\tilde …

In this thesis, we present a new method to solve algorithmic and combinatorial problems by
(1) reducing them to bounding the maximum, over 𝑥∈{− 1, 1} 𝑛, of homogeneous degree-𝑞 …