Chromatic Polynomials of Mixed Hypercycles
Julian A. Allagan ; David Slutzky
Discussiones Mathematicae Graph Theory, Tome 34 (2014), p. 547-558 / Harvested from The Polish Digital Mathematics Library

We color the vertices of each of the edges of a C-hypergraph (or cohypergraph) in such a way that at least two vertices receive the same color and in every proper coloring of a B-hypergraph (or bihypergraph), we forbid the cases when the vertices of any of its edges are colored with the same color (monochromatic) or when they are all colored with distinct colors (rainbow). In this paper, we determined explicit formulae for the chromatic polynomials of C-hypercycles and B-hypercycles

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:267673
@article{bwmeta1.element.doi-10_7151_dmgt_1750,
     author = {Julian A. Allagan and David Slutzky},
     title = {Chromatic Polynomials of Mixed Hypercycles},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {34},
     year = {2014},
     pages = {547-558},
     zbl = {1305.05066},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1750}
}
Julian A. Allagan; David Slutzky. Chromatic Polynomials of Mixed Hypercycles. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 547-558. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1750/

[1] J.A. Allagan, The chromatic polynomials of some linear uniform hypergraphs, Congr. Numer. 187 (2007) 156-160.[WoS] | Zbl 1133.05029

[2] C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam, 1973).

[3] A.A. Bhatti, S.A. Bokhary and I. Tomescu, On the chromaticity of multi-bridge hypergraphs, Graphs Combin. 25 (2009) 145-152. doi:10.1007/s00373-008-0831-7[Crossref] | Zbl 1213.05065

[4] M. Borowiecki and E. Lazuka, On chromaticity of hypergraphs, Discrete Math. 307 (2007) 1418-1429. doi:10.1016/j.disc.2005.11.079[WoS][Crossref] | Zbl 1119.05040

[5] M. Borowiecki and E. Lazuka, Chromatic polynomials of hypergraphs, Discuss. Math. Graph Theory 20 (2000) 293-301. doi:10.7151/dmgt.1128[Crossref] | Zbl 0979.05044

[6] F.M. Dong, K.M. Koh and K.L. Teo, Chromatic Polynomials and Chromaticity of Graphs (Company Singapore: World Scientific Publishing., 2005). | Zbl 1070.05038

[7] G. Lo Faro, L. Milazzo and A. Tripodi, On the upper and lower chromatic number of BSQSS(16), Electron. J. Combin. 8 (2001)#R6. | Zbl 0974.05034

[8] M. Gionfriddo, L. Milazzo, A. Rosa and V. Voloshin, Bicolouring Steiner systems S(2, 4, v), Discrete Math. 283 (2004) 249-253. doi:10.1016/j.disc.2003.11.016[Crossref] | Zbl 1044.05018

[9] D. Kr´al’, J. Kratochvil and H. Voss, Mixed hypercacti, Discrete Math. 286 (2004) 99-113. doi:10.1016/j.disc.2003.11.051[Crossref] | Zbl 1064.05060

[10] T. Jiang, D. Mubayi, Zs. Tuza, V. Voloshin and D.B. West, The chromatic spectrum of mixed hypergraphs, Graphs Combin. 18 (2002) 309-318. doi:10.1007/s003730200023[Crossref]

[11] L. Milazzo and Zs. Tuza, Upper chromatic number of Steiner triple and quadruple systems, Discrete Math. 174 (1997) 247-259. doi:10.1016/S0012-365X(97)80332-9[Crossref] | Zbl 0901.05012

[12] L. Milazzo and Zs. Tuza, Strict colouring for classes of Steiner triple systems, Discrete Math. 182 (1998) 233-243. doi:10.1016/S0012-365X(97)00143-X[Crossref]

[13] L. Milazzo, Zs. Tuza and V. Voloshin, Strict coloring of triple and quadruple Steiner systems: a survey, Discrete Math. 261 (2003) 399-411. doi:10.1016/S0012-365X(02)00485-5[Crossref] | Zbl 1008.05025

[14] L. Milazzo and Zs. Tuza, Logarithmic upper bound for upper chromatic number of S(t, t + 1, v) systems, Ars Combin. 92 (2009) 213-223. | Zbl 1224.05183

[15] I. Tomescu, Chromatic coefficients of linear uniform hypergraphs, J. Combin. Theory (B) 72 (1998) 229-235. doi:10.1006/jctb.1997.1811[WoS][Crossref]

[16] V.I. Voloshin, The mixed hypergraphs, Comput. Sci. J. Moldova 1 (1993) 45-52.

[17] V.I. Voloshin, On the upper chromatic number of a hypergraph, Australas. J. Combin. 11 (1995) 25-45. | Zbl 0827.05027

[18] V.I. Voloshin, Coloring Mixed Hypergraphs: Theory, Algorithms and Applications (American Mathematical Society, Providence 2002). | Zbl 1001.05003

[19] M.Walter, Some results on chromatic polynomials of hypergraphs, Electron. J. Combin. 16 (2009) #R94. | Zbl 1186.05059