TY - JOUR
T1 - Codegree conditions for cycle decompositions and Euler tours in 3-uniform hypergraphs
AU - Piga, Simon
AU - Sanhueza-Matamala, Nicolás
PY - 2022/1/5
Y1 - 2022/1/5
N2 - We show that 3-graphs whose codegree is at least (2/3 + o(1))n can be decomposed into tight cycles and admit Euler tours, subject to the trivial necessary divisibility conditions. We also provide a construction showing that our bounds are best possible up to the o(1) term. All together, our results answer in the negative some recent questions of Glock, Joos, Kühn and Osthus.
AB - We show that 3-graphs whose codegree is at least (2/3 + o(1))n can be decomposed into tight cycles and admit Euler tours, subject to the trivial necessary divisibility conditions. We also provide a construction showing that our bounds are best possible up to the o(1) term. All together, our results answer in the negative some recent questions of Glock, Joos, Kühn and Osthus.
KW - Cycles
KW - Decompositions
KW - Euler tours
KW - Hypergraphs
UR - https://arxiv.org/abs/2101.12205
U2 - 10.1016/j.procs.2021.11.043
DO - 10.1016/j.procs.2021.11.043
M3 - Article
SN - 1877-0509
VL - 195
SP - 350
EP - 358
JO - Procedia Computer Science
JF - Procedia Computer Science
ER -