Minimum vertex degree conditions for loose Hamilton cycles in 3-uniform hypergraphs

Autor(es)

Buss, Enno ^[1] ; Han, Hiep ^[1] ; Schacht, Mathias ^[1]

Afiliação do(s) autor(es)

^[1] Univ Hamburg, Fachbereich Math, D-20146 Hamburg - Germany

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF COMBINATORIAL THEORY SERIES B; v. 103, n. 6, p. 658-678, NOV 2013.
• Citações Web of Science: 13

Resumo

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 only consecutive edges intersect and these intersections consist of precisely one vertex. We prove that every 3-uniform n-vertex (n even) hypergraph H with minimum vertex degree delta(1)(H) >= (7/16 + o(1))((n)(2)) contains a loose Hamilton cycle. This bound is asymptotically best possible. (C) 2013 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 10/16526-3 - Hipergrafos quase-aleatórios e imersão de subhipergrafos geradores
• Beneficiário: Hiep Han
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado