As a natural generalization of Dirac's theorem, Pósa conjectured the following in 1962. Conjecture 1 (P´osa). Let G be a graph on n vertices. If δ(G) ≥ 2. 3.
Paul Seymour conjectured that any graph G of order n and minimum degree at least contains the kth power of a Hamilton cycle. We prove the following ...
Jul 22, 2023 · In this paper, they authors make a significant step towards proving a hypergraph version of this difficult problem.
Oct 18, 2021 · This result may be seen as a step towards a hypergraph version of the Pósa-Seymour conjecture. Moreover, we prove that the same bound on the ...
Paul Seymour conjectured that any graph G of order n and minimum degree at least k/k+1 n contains the kth power of a Hamilton cycle. We prove the following ...
Paul Seymour conjectured that any graph G of order n and minimum degree at least $\frac{k}{k+1}n$ contains the kth power of a Hamilton cycle.
Dec 24, 2024 · The Pósa--Seymour conjecture determines the minimum degree threshold for forcing the kth power of a Hamilton cycle in a graph. After numerous ...
Video library: E. Szemeredi, Proof of the Pósa--Seymour Conjecture
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Abstract: In 1974 Paul Seymour conjectured that any graph G of order n and minimum degree at least (k−1)/k⋅n contains the (k−1)th power of k a ...
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This result may be seen as a step towards a hypergraph version of the Pósa-Seymour conjecture. Moreover, we prove that the same bound on the codegree ...
Jul 20, 2012 · The famous Pósa conjecture states that every graph of minimum degree at least 2n/3 contains the square of a Hamilton cycle. This has been proved ...