Zero-free intervals of chromatic polynomials of hypergraphs

Abstract In this paper, we prove that ( − ∞ , 0 ) is a zero-free interval for chromatic polynomials of a family L 0 of hypergraphs and ( 0 , 1 ) is a zero-free interval for chromatic polynomials of a subfamily L 0 ′ of L 0 of hypergraphs. These results extend known results on zero-free intervals of chromatic polynomials of graphs and hypergraphs.

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

[2]  P. Erdos,et al.  On chromatic number of graphs and set-systems , 1966 .

[3]  Carsten Thomassen,et al.  The Zero-Free Intervals for Chromatic Polynomials of Graphs , 1997, Combinatorics, Probability and Computing.

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

[5]  Kinoshita Hirotsugu,et al.  Access Control Model for the Inference Attacks with Access Histories , 2017, 2017 IEEE 41st Annual Computer Software and Applications Conference (COMPSAC).

[6]  Ioan Tomescu.  Hypergraphs with Pendant Paths are not Chromatically Unique , 2014, Discuss. Math. Graph Theory.

[7]  Julian A. Allagan.  Chromatic Polynomials Of Some (m, l)-Hyperwheels , 2014, Comput. Sci. J. Moldova.

[8]  G. F. Royle.  Surveys in Combinatorics 2009: Recent results on chromatic and flow roots of graphs and matroids , 2009 .

[9]  Alan D. Sokal,et al.  Chromatic Roots are Dense in the Whole Complex Plane , 2000, Combinatorics, Probability and Computing.

[10]  Siddhartha Sen,et al.  On the price of equivocation in byzantine agreement , 2012, PODC '12.

[11]  Ruixue Zhang,et al.  Properties of chromatic polynomials of hypergraphs not held for chromatic polynomials of graphs , 2016, Eur. J. Comb..

[12]  Klaus Dohmen,et al.  A Broken-Circuits-Theorem for hypergraphs , 1995 .

[13]  Daniel Král.  Mixed hypergraphs and other coloring problems , 2007, Discret. Math..

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

[15]  M. Halldórsson,et al.  Strong Colorings of Hypergraphs , 2004, WAOA.

[16]  R. Read.  An introduction to chromatic polynomials , 1968 .

[17]  Vitaly I. Voloshin,et al.  On the upper chromatic number of a hypergraph , 1995, Australas. J Comb..

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

[19]  N. Biggs.  Algebraic Graph Theory , 1974 .

[20]  Julian A. Allagan,et al.  Chromatic polynomials of some mixed hypergraphs , 2014, Australas. J Comb..

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

[22]  Rhys Price Jones.  Colourings of hypergraphs , 1976 .

[23]  Bill Jackson,et al.  A Zero-Free Interval for Chromatic Polynomials of Nearly 3-Connected Plane Graphs , 2011, SIAM J. Discret. Math..

[24]  Bill Jackson,et al.  Zeros of chromatic and flow polynomials of graphs , 2002, math/0205047.

[25]  Bill Jackson,et al.  A Zero-Free Interval for Chromatic Polynomials of Graphs , 1993, Combinatorics, Probability and Computing.

[26]  Carsten Thomassen.  Chromatic Roots and Hamiltonian Paths , 2000, J. Comb. Theory, Ser. B.

[27]  V. Voloshin.  Coloring mixed hypergraphs : theory, algorithms and applications , 2002 .

[28]  Lei Yu,et al.  Towards a Restrained Use of Non-Equivocation for Achieving Iterative Approximate Byzantine Consensus , 2016, 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS).

[29]  Ioan Tomescu,et al.  Some Properties of Chromatic Coefficients of Linear Uniform Hypergraphs , 2009, Graphs Comb..

[30]  H. Whitney.  A logical expansion in mathematics , 1932 .

[31]  Vitaly I. Voloshin,et al.  The mixed hypergraphs , 1993, Comput. Sci. J. Moldova.

[32]  Manfred Walter.  Some Results on Chromatic Polynomials of Hypergraphs , 2009, Electron. J. Comb..

[33]  Douglas R. Woodall.  The largest real zero of the chromatic polynomial , 1997, Discret. Math..