A note on a broken-cycle theorem for hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 641-646.

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Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there.
Keywords: Broken-cycle Theorem, hypergraphs, cycles, chromatic polynomial, graph polynomials
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Trinks, Martin. A note on a broken-cycle theorem for hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 641-646. http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a17/

[1] C. Berge, Hypergraphs, Vol. 45 (North-Holland Mathematical Library, North-Holland, 1989).

[2] K. Dohmen, A broken-circuits-theorem for hypergraphs, Arch. Math. 64 (1995) 159-162. doi:10.1007/BF01196637

[3] F.M. Dong, K.M. Koh, and K.L. Teo, Chromatic polynomials and chromaticity of graphs (World Scientific Publishing, 2005).

[4] P. Jégou and S.N. Ndiaye, On the notion of cycles in hypergraphs, Discrete Math. 309 (2009) 6535-6543. doi:10.1016/j.disc.2009.06.035

[5] M. Trinks, Graph polynomials and their representations, PhD Thesis, Technische Universität Bergakademie Freiberg, (2012).

[6] H. Whitney, The coloring of graphs, Proc. Natl. Acad. Sci. USA 17(2) (1931) 122-125. doi:10.1073/pnas.17.2.122

[7] H. Whitney, A logical expansion in mathematics, Bull. Amer. Math. Soc. 38(8) (1932) 572-579. doi:10.1090/S0002-9904-1932-05460-X