Antichains in the cycle continuous order ★★

Author(s): DeVos

If $G$,$H$ are graphs, a function $f : E(G) \rightarrow E(H)$ is called \emph{cycle-continuous} if the pre-image of every element of the (binary) cycle space of $H$ is a member of the cycle space of $G$.

\begin{problem} Does there exist an infinite set of graphs $\{G_1,G_2,\ldots \}$ so that there is no cycle continuous mapping between $G_i$ and $G_j$ whenever $i \neq j$ ? \end{problem}

Keywords: antichain; cycle; poset

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