in the Cycle-Continuous Order
in a graph is a subgraph with each vertex of even degree. A map f : E(G) -> E(H)
if the preimage of
any cycle is a cycle. We write G
if there is a cycle-continuous map from G
. It is easy to see that this
order is reflexive and transitive. For example, if A_k
is the graph with 2 vertices
parallel edges, then A_3 < A_5 < A_7 < ...
an infinite chain.
To my knowledge, Matt DeVos introduced this order (see The
Petersen coloring conjecture
). Apparently little is known about it.
DeVos asks the following:
Question: Does there exist an infinite antichain in
the cycle-continuous order?
Submitted by: Dan Archdeacon, Department of
and Statistics, University of Vermont, Burlington VT 05405 USA. (with thanks to Matt DeVos)
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