Some Results on Chromatic Polynomials of Hypergraphs

In this paper, chromatic polynomials of (non-uniform) hypercycles, unicyclic hypergraphs, hypercacti and sunflower hypergraphs are presented. The formulae generalize known results for r-uniform hypergraphs due to Allagan, Borowiecki/ Lazuka, Dohmen and Tomescu. Furthermore, it is shown that the class of (non-uniform) hypertrees with m edges, where mr edges have size r, r 2, is chromatically closed if and only if m 4, m2 m 1.

[1]  Julian A. Allagan.  A generalization of the chromatic polynomial of a cycle , 2005, Comput. Sci. J. Moldova.

[2]  Ioan Tomescu.  Sunflower hypergraphs are chromatically unique , 2004, Discret. Math..

[3]  Martin Sonntag,et al.  Antimagic vertex labelings of hypergraphs , 2002, Discret. Math..

[4]  Ewa Lazuka,et al.  On chromaticity of graphs , 1995, Discuss. Math. Graph Theory.

[5]  K. Koh,et al.  Chromatic polynomials and chro-maticity of graphs , 2005 .

[6]  Martin Sonntag.  A characterization of hypercacti , 2007, Discret. Math..

[7]  Ioan Tomescu.  On the chromaticity of sunflower hypergraphs SH(n, p, h) , 2007, Discret. Math..

[8]  Ewa Łazuka,et al.  On chromaticity of graphs , 1995 .

[9]  Mieczyslaw Borowiecki,et al.  Chromatic polynomials of hypergraphs , 2006, Discuss. Math. Graph Theory.

[10]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[11]  Mieczyslaw Borowiecki,et al.  On chromaticity of hypergraphs , 2007, Discret. Math..

[12]  Ioan Tomescu,et al.  Chromatic Coefficients of Linear Uniform Hypergraphs , 1998, J. Comb. Theory, Ser. B.