Gábor N. Sárközy

Publications114
h-index29
Citations2,425
Highly Influential Citations336
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Blow-up Lemma
Regular pairs behave like complete bipartite graphs from the point of view of bounded degree subgraphs.
Proof of the Alon-Yuster conjecture
Proof of the Seymour conjecture for large graphs
Paul Seymour conjectured that any graphG of ordern and minimum degree of at leastk/k+1n contains thekth power of a Hamiltonian cycle. Here, we prove this conjecture for sufficiently largen.
An improved bound for the monochromatic cycle partition number
On the Pósa-Seymour conjecture
TLDR
The following approximate version of Paul Seymour's conjecture is proved: for any > 0 and positive integer k, there is an n0 such that, if G has order n ≥ n0 and minimum degree at least ( k k+1 + )n, then G contains the kth power of a Hamilton cycle.
Three-Color Ramsey Numbers For Paths
TLDR
It is proved that for sufficiently large n, for the three-color Ramsey numbers of paths on n vertices, the following conjecture of Faudree and Schelp is proved.
How to avoid using the Regularity Lemma: Pósa's conjecture revisited
An algorithmic version of the blow-up lemma
TLDR
This paper provides an algorithmic version of the Blow-up Lemma, which helps to find bounded degree spanning subgraphs in $\varepsilon$-regular graphs and can be parallelized and implemented in $NC^5$.
Proof of a Packing Conjecture of Bollobás
TLDR
Here it is proved that for any positive integer Δ and real 0 c n 0, T is a tree of order n and maximum degree Δ, and G is a graph ofOrder n andmaximum degree not exceeding cn , then there is a packing of T and G.
Ramsey‐type results for Gallai colorings
TLDR
It is proved that in every G-coloring of Kn there exists each of the following: a monochromatic double star with at least 3n+1 4 vertices; and RG(r,K3) can be determined exactly.
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