The notion of robust expansion has played a central role in the solution of several conjectures involving the packing of Hamilton cycles in graphs and directed graphs. These and other results usually rely on the fact that every robustly expanding (di)graph with suitably large minimum degree contains a Hamilton cycle. Previous proofs of this require Szemerédi's Regularity Lemma and so this fact can only be applied to dense, sufficiently large robust expanders. We give a proof that does not use the Regularity Lemma and, indeed, we can apply our result to sparser robustly expanding digraphs.
@article{10_37236_7418,
author = {Allan Lo and Viresh Patel},
title = {Hamilton cycles in sparse robustly expanding digraphs},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {3},
doi = {10.37236/7418},
zbl = {1395.05072},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7418/}
}
TY - JOUR
AU - Allan Lo
AU - Viresh Patel
TI - Hamilton cycles in sparse robustly expanding digraphs
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/7418/
DO - 10.37236/7418
ID - 10_37236_7418
ER -
%0 Journal Article
%A Allan Lo
%A Viresh Patel
%T Hamilton cycles in sparse robustly expanding digraphs
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/7418/
%R 10.37236/7418
%F 10_37236_7418
Allan Lo; Viresh Patel. Hamilton cycles in sparse robustly expanding digraphs. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7418
