Localized Codegree Conditions for Tight Hamilton Cycles in 3-Uniform Hypergraphs

2022 ◽  
Vol 36 (1) ◽  
pp. 147-169
Author(s):  
Pedro Araújo ◽  
Simón Piga ◽  
Mathias Schacht
Keyword(s):  
Hamilton Cycles ◽  
Uniform Hypergraphs

scholarly journals Packing tight Hamilton cycles in 3-uniform hypergraphs

2011 ◽  
Vol 40 (3) ◽  
pp. 269-300 ◽  
Author(s):  
Alan Frieze ◽  
Michael Krivelevich ◽  
Po-Shen Loh
Keyword(s):  
Hamilton Cycles ◽  
Uniform Hypergraphs

scholarly journals Loose Hamilton Cycles in Random 3-Uniform Hypergraphs

10.37236/477 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Alan Frieze
Keyword(s):  
Absolute Constant ◽  
Hamilton Cycle ◽  
Hamilton Cycles ◽  
Uniform Hypergraphs ◽  
Random Hypergraph

In the random hypergraph $H=H_{n,p;3}$ each possible triple appears independently with probability $p$. A loose Hamilton cycle can be described as a sequence of edges $\{x_i,y_i,x_{i+1}\}$ for $i=1,2,\ldots,n/2$ where $x_1,x_2,\ldots,x_{n/2},y_1,y_2,\ldots,y_{n/2}$ are all distinct. We prove that there exists an absolute constant $K>0$ such that if $p\geq {K\log n\over n^2}$ then $$\lim_{\textstyle{n\to \infty\atop 4|n}}\Pr(H_{n,p;3}\ contains\ a\ loose\ Hamilton\ cycle)=1.$$

scholarly journals Matchings and Hamilton cycles in hypergraphs

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Daniela Kühn ◽  
Deryk Osthus
Keyword(s):  
Bipartite Graph ◽  
Perfect Matching ◽  
Minimum Degree ◽  
Hamilton Cycle ◽  
Uniform Hypergraph ◽  
Hamilton Cycles ◽  
Uniform Hypergraphs ◽  
International Audience

International audience It is well known that every bipartite graph with vertex classes of size $n$ whose minimum degree is at least $n/2$ contains a perfect matching. We prove an analogue of this result for uniform hypergraphs. We also provide an analogue of Dirac's theorem on Hamilton cycles for $3$-uniform hypergraphs: We say that a $3$-uniform hypergraph has a Hamilton cycle if there is a cyclic ordering of its vertices such that every pair of consecutive vertices lies in a hyperedge which consists of three consecutive vertices. We prove that for every $\varepsilon > 0$ there is an $n_0$ such that every $3$-uniform hypergraph of order $n \geq n_0$ whose minimum degree is at least $n/4+ \varepsilon n$ contains a Hamilton cycle. Our bounds on the minimum degree are essentially best possible.

scholarly journals Packing Tight Hamilton Cycles in Uniform Hypergraphs

2012 ◽  
Vol 26 (2) ◽  
pp. 435-451 ◽  
Author(s):  
Deepak Bal ◽  
Alan Frieze
Keyword(s):  
Hamilton Cycles ◽  
Uniform Hypergraphs

Extensions of Results on Rainbow Hamilton Cycles in Uniform Hypergraphs

2013 ◽  
Vol 31 (3) ◽  
pp. 577-583 ◽  
Author(s):  
Andrzej Dudek ◽  
Michael Ferrara
Keyword(s):  
Hamilton Cycles ◽  
Uniform Hypergraphs
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