Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Rudd, Jason D. 2010. Tutte polynomials for counting and classifying orbits. Discrete Mathematics, Vol. 310, Issue. 2, p. 206.

    Cameron, Peter J. Jackson, Bill and Rudd, Jason D. 2008. Orbit-counting polynomials for graphs and codes. Discrete Mathematics, Vol. 308, Issue. 5-6, p. 920.


Orbital Chromatic and Flow Roots

  • PETER J. CAMERON (a1) and K. K. KAYIBI (a1)
  • DOI:
  • Published online: 01 May 2007

The chromatic polynomial PΓ(x) of a graph Γ is a polynomial whose value at the positive integer k is the number of proper k-colourings of Γ. If G is a group of automorphisms of Γ, then there is a polynomial OPΓ,G(x), whose value at the positive integer k is the number of orbits of G on proper k-colourings of Γ.

It is known that real chromatic roots cannot be negative, but they are dense in ∞). Here we discuss the location of real orbital chromatic roots. We show, for example, that they are dense in , but under certain hypotheses, there are zero-free regions.

We also look at orbital flow roots. Here things are more complicated because the orbit count is given by a multivariate polynomial; but it has a natural univariate specialization, and we show that the roots of these polynomials are dense in the negative real axis.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[2]B. Jackson (1993) A zero-free interval for chromatic polynomials of graphs. Combin. Probab. Comput. 2 325336.

[4]A. D. Sokal (2004) Chromatic roots are dense in the whole complex plane. Combin. Probab. Comput. 13 221261.

[5]C. Thomassen (1997) The zero-free intervals for chromatic polynomials of graphs. Combin. Probab. Comput. 6 497506.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
Please enter your name
Please enter a valid email address
Who would you like to send this to? *