Minimum Vertex Degree Conditions for Loose Hamilton Cycles in 3-uniform Hypergraphs
نویسنده
چکیده
We investigate minimum vertex degree conditions for 3-uniform hypergraphs which ensure the existence of loose Hamilton cycles. A loose Hamilton cycle is a spanning cycle in which consecutive edges intersect in a single vertex. We prove that every 3-uniform n-vertex (n even) hypergraph H with minimum vertex degree δ1(H) ≥ ( 7 16 + o(1) ) (n 2 ) contains a loose Hamilton cycle. This bound is asymptotically best possible.
منابع مشابه
Minimum vertex degree conditions for loose Hamilton cycles in 3-uniform hypergraphs
We investigate minimum vertex degree conditions for 3-uniform hypergraphs which ensure the existence of loose Hamilton cycles. A loose Hamilton cycle is a spanning cycle in which consecutive edges intersect in a single vertex. We prove that every 3-uniform n-vertex (n even) hypergraph H with minimum vertex degree δ1(H) ≥ ( 7 16 + o(1) ) ( n 2 ) contains a loose Hamilton cycle. This bound is asy...
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