A Note on a Broken-Cycle Theorem for Hypergraphs

Martin Trinks

Discussiones Mathematicae Graph Theory (2014)

  • Volume: 34, Issue: 3, page 641-646
  • ISSN: 2083-5892

Abstract

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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

How to cite

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Martin Trinks. "A Note on a Broken-Cycle Theorem for Hypergraphs." Discussiones Mathematicae Graph Theory 34.3 (2014): 641-646. <http://eudml.org/doc/267958>.

@article{MartinTrinks2014,
abstract = {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},
author = {Martin Trinks},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {Broken-cycle Theorem; hypergraphs; cycles; chromatic polynomial; graph polynomials; broken-cycle theorem},
language = {eng},
number = {3},
pages = {641-646},
title = {A Note on a Broken-Cycle Theorem for Hypergraphs},
url = {http://eudml.org/doc/267958},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Martin Trinks
TI - A Note on a Broken-Cycle Theorem for Hypergraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 3
SP - 641
EP - 646
AB - 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
LA - eng
KW - Broken-cycle Theorem; hypergraphs; cycles; chromatic polynomial; graph polynomials; broken-cycle theorem
UR - http://eudml.org/doc/267958
ER -

References

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  1. [1] C. Berge, Hypergraphs, Vol. 45 (North-Holland Mathematical Library, North- Holland, 1989). 
  2. [2] K. Dohmen, A broken-circuits-theorem for hypergraphs, Arch. Math. 64 (1995) 159-162. doi:10.1007/BF01196637[Crossref] Zbl0813.05048
  3. [3] F.M. Dong, K.M. Koh, and K.L. Teo, Chromatic polynomials and chromaticity of graphs (World Scientific Publishing, 2005). Zbl1070.05038
  4. [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] Zbl1229.05172
  5. [5] M. Trinks, Graph polynomials and their representations, PhD Thesis, Technische Universität Bergakademie Freiberg, (2012). 
  6. [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] Zbl0001.29301
  7. [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] Zbl0005.14602

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