I am investigating whether the following hypergraph is $2$-colorable.

Let $0\le c &lt; d &lt; e$ be fixed natural numbers and consider a graph on $2e$ vertices, with the vertices labelled as $0,1,\cdots 2e-1$. For every vertex $u$, whenever $u+x-y$ and $u+z-y$ make sense as a vertex and $x,y,z$ are such that $\{x,y,z\}=\{c,d,e\}$, there is a hyperedge $\{u,u+x-y,u+z-y\}$. Is this graph $2$-colorable? If so, how can I construct a $2$-coloring?

I'll be grateful for any suggestions or comments.


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