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 -