A Note on a Broken-Cycle Theorem for Hypergraphs

• Autorzy: Martin Trinks
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Broken-cycle Theorem; hypergraphs; cycles; chromatic polynomial; graph polynomials

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 3
• Strony: 641-646

Daty

wydano

2014-08-01

otrzymano

2012-10-04

zaakceptowano

2013-02-14

online

2014-07-16

Twórcy

autor

Martin Trinks

• Hochschule Mittweida, University of Applied Sciences Faculty Mathematics / Sciences / Computer Science Technikumplatz 17, 09648 Mittweida, Germany

Bibliografia

• [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]
• [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[Crossref]
• [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]
• [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]

Identyfikatory

DOI

10.7151/dmgt.1734