Both Cuckler and Yuster independently conjectured that when $n$ is an odd positive multiple of $3$ every regular tournament on $n$ vertices contains a collection of $n/3$ vertex-disjoint copies of the cyclic triangle. Soon after, Keevash \& Sudakov proved that if $G$ is an orientation of a graph on $n$ vertices in which every vertex has both indegree and outdegree at least $(1/2 - o(1))n$, then there exists a collection of vertex-disjoint cyclic triangles that covers all but at most $3$ vertices. In this paper, we resolve the conjecture of Cuckler and Yuster for sufficiently large $n$.
@article{10_37236_7759,
author = {Lina Li and Theodore Molla},
title = {Cyclic triangle factors in regular tournaments},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/7759},
zbl = {1432.05082},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7759/}
}
TY - JOUR
AU - Lina Li
AU - Theodore Molla
TI - Cyclic triangle factors in regular tournaments
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/7759/
DO - 10.37236/7759
ID - 10_37236_7759
ER -
%0 Journal Article
%A Lina Li
%A Theodore Molla
%T Cyclic triangle factors in regular tournaments
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/7759/
%R 10.37236/7759
%F 10_37236_7759
Lina Li; Theodore Molla. Cyclic triangle factors in regular tournaments. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/7759
