Geodesic
A polynomial time algorithm for checking $2$-chromaticity for recursively constructed $k$-terminal hypergraphs
Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 80-85

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It is shown that for $k$-terminal recursively constructed hypergraphs the $2$-colorability problem: for a given hypergraph $H$ to find out whether there exists a coloring $f\colon V(H)\to\{1,2\}$ such that no edge of $H$ is monochromatic, can be solved in $O(n^3)$ time. 
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     author = {V. V. Lepin},
     title = {A polynomial time algorithm for checking $2$-chromaticity for recursively constructed $k$-terminal hypergraphs},
     journal = {Trudy Instituta matematiki},
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     volume = {14},
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     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a9/}
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V. V. Lepin. A polynomial time algorithm for checking $2$-chromaticity for recursively constructed $k$-terminal hypergraphs. Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 80-85. http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a9/