A Note on a Broken-Cycle Theorem for Hypergraphs
Martin Trinks
Discussiones Mathematicae Graph Theory, Tome 34 (2014), p. 641-646 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:267958 
@article{bwmeta1.element.doi-10_7151_dmgt_1734,
     author = {Martin Trinks},
     title = {A Note on a Broken-Cycle Theorem for Hypergraphs},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {34},
     year = {2014},
     pages = {641-646},
     zbl = {1305.05106},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1734}
}

Martin Trinks. A Note on a Broken-Cycle Theorem for Hypergraphs. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 641-646. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1734/

[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[Crossref] | Zbl 0813.05048

[3] F.M. Dong, K.M. Koh, and K.L. Teo, Chromatic polynomials and chromaticity of graphs (World Scientific Publishing, 2005). | Zbl 1070.05038

[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[Crossref] | Zbl 1229.05172

[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[Crossref] | Zbl 0001.29301

[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[Crossref] | Zbl 0005.14602