Hypergraphs with Pendant Paths are not Chromatically Unique
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 23-29.

Voir la notice de l'article provenant de la source Library of Science

In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.
Keywords: sunflower hypergraph, chromatic polynomial, pendant path, chromatic uniqueness
@article{DMGT_2014_34_1_a1,
     author = {Tomescu, Ioan},
     title = {Hypergraphs with {Pendant} {Paths} are not {Chromatically} {Unique}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {23--29},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a1/}
}
TY  - JOUR
AU  - Tomescu, Ioan
TI  - Hypergraphs with Pendant Paths are not Chromatically Unique
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2014
SP  - 23
EP  - 29
VL  - 34
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a1/
LA  - en
ID  - DMGT_2014_34_1_a1
ER  - 
%0 Journal Article
%A Tomescu, Ioan
%T Hypergraphs with Pendant Paths are not Chromatically Unique
%J Discussiones Mathematicae. Graph Theory
%D 2014
%P 23-29
%V 34
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a1/
%G en
%F DMGT_2014_34_1_a1
Tomescu, Ioan. Hypergraphs with Pendant Paths are not Chromatically Unique. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 23-29. http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a1/

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

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

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

[4] C.Y. Chao and E.G. Whitehead, Jr., On chromatic equivalence of graphs, in: Theory and Applications of Graphs, Y. Alavi and D.R. Lick (Ed(s)), (Lecture Notes Math. 642, New York, Springer (1978)) 121-131.

[5] D. Dellamonica, V. Koubek, D.M. Martin and V. Rödl, On a conjecture of Thomassen concerning subgraphs of large girth, J. Graph Theory 67 (2011) 316-331. doi:10.1002/jgt.20534

[6] K. Dohmen, Chromatische Polynome von Graphen und Hypergraphen (Dissertation, Düsseldorf, 1993).

[7] P. Erdős and R. Rado, Intersection theorems for systems of sets, J. Lond. Math. Soc. 35 (1960) 85-90. doi:10.1112/jlms/s1-35.1.85

[8] Z. Füredi, On finite set-systems whose intersection is a kernel of a star, Discrete Math. 47 (1983) 129-132. doi:10.1016/0012-365X(83)90081-X

[9] K.M. Koh and K.L. Teo, The search for chromatically unique graphs, Graphs Combin. 6 (1990) 259-285. doi:10.1007/BF01787578

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

[11] I. Tomescu, Sunflower hypergraphs are chromatically unique, Discrete Math. 285 (2004) 355-357. doi:10.1016/j.disc.2004.02.015

[12] I. Tomescu, On the chromaticity of sunflower hypergraphs SH(n, p, h), Discrete Math. 307 (2007) 781-786. doi:10.1016/j.disc.2006.07.026

[13] I. Tomescu and S. Javed, On the chromaticity of quasi linear hypergraphs, Graphs Combin. 29 (2013) 1921-1026. doi:10.1007/s00373-012-1232-5

[14] M. Walter, Some results on chromatic polynomials of hypergraphs, Electron. J. Combin. 16 (2009) R94.