We study the following conjecture of Matt DeVos: If there is a graph homomorphism from a Cayley graph $\mathrm{Cay}(M, B)$ to another Cayley graph $\mathrm{Cay}(M', B')$ then every graph with an $(M,B)$-flow has an $(M',B')$-flow. This conjecture was originally motivated by the flow-tension duality. We show that a natural strengthening of this conjecture does not hold in all cases but we conjecture that it still holds for an interesting subclass of them and we prove a partial result in this direction. We also show that the original conjecture implies the existence of an oriented cycle double cover with a small number of cycles.
@article{10_37236_8456,
author = {Radek Hu\v{s}ek and Robert \v{S}\'amal},
title = {Homomorphisms of {Cayley} graphs and cycle double covers},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {2},
doi = {10.37236/8456},
zbl = {1443.05129},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8456/}
}
TY - JOUR
AU - Radek Hušek
AU - Robert Šámal
TI - Homomorphisms of Cayley graphs and cycle double covers
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/8456/
DO - 10.37236/8456
ID - 10_37236_8456
ER -
%0 Journal Article
%A Radek Hušek
%A Robert Šámal
%T Homomorphisms of Cayley graphs and cycle double covers
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/8456/
%R 10.37236/8456
%F 10_37236_8456
Radek Hušek; Robert Šámal. Homomorphisms of Cayley graphs and cycle double covers. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8456
