Hypergraph extensions of the Erdős-Gallai Theorem - ScienceDirect Skip to main contentSkip to
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We prove that for integers $2\leq\ell< k $ and a small constant $ c $, if a $ k $-uniform
hypergraph with linear minimum codegree is randomlyperturbed'by changing non-edges to …

In this paper, we develop a new rainbow Hamilton framework, which is of independent
interest, settling the problem proposed by Gupta, Hamann, M\"{u} yesser, Parczyk, and …

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A tight cycle in an-uniform hypergraph is a sequence of vertices such that all-tuples (with
subscripts modulo) are edges of. An old problem of V. Sós, also posed independently by J …

We develop a new framework to study minimum dd‐degree conditions in kk‐uniform
hypergraphs, which guarantee the existence of a tight Hamilton cycle. Our main theoretical …

A cornerstone of extremal graph theory due to Erd\H {o} s and Stone states that the edge
density which guarantees a fixed graph $ F $ as subgraph also asymptotically guarantees a …

We show that every $ r $-uniform hypergraph on $ n $ vertices which does not contain a tight
cycle has at most $ O (n^{r-1}(\log n)^ 5) $ edges. This is an improvement on the previously …

Abstract Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is
very fast developing, and in this long but relatively short survey we select some of those …

We prove that for fixed $ r\ge k\ge 2$, every $ k $-uniform hypergraph on $ n $ vertices
having minimum codegree at least $(1-(\binom {r-1}{k-1}+\binom {r-2}{k-2})^{-1}) n+ o (n) …