TY - JOUR

T1 - The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph

AU - Cooley, Oliver Josef Nikolaus

AU - Mycroft, Richard

PY - 2017

Y1 - 2017

N2 - We prove that any 3-uniform hypergraph whose minimum vertex degree is at least 59+o(1)n2 admits an almost-spanning tight cycle, that is, a tight cycle leaving o(n) vertices uncovered. The bound on the vertex degree is asymptotically best possible. Our proof uses the hypergraph regularity method, and in particular a recent version of the hypergraph regularity lemma proved by Allen, Böttcher, Cooley and Mycroft.

AB - We prove that any 3-uniform hypergraph whose minimum vertex degree is at least 59+o(1)n2 admits an almost-spanning tight cycle, that is, a tight cycle leaving o(n) vertices uncovered. The bound on the vertex degree is asymptotically best possible. Our proof uses the hypergraph regularity method, and in particular a recent version of the hypergraph regularity lemma proved by Allen, Böttcher, Cooley and Mycroft.

U2 - 10.1016/j.disc.2016.12.015

DO - 10.1016/j.disc.2016.12.015

M3 - Article

VL - 340

SP - 1172

EP - 1179

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 6

ER -