Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-28T21:30:43.350Z Has data issue: false hasContentIssue false
  • English
  • Français

The Tutte Polynomial Characterizes Simple Outerplanar Graphs

Published online by Cambridge University Press:  09 March 2011

A. J. GOODALL ,
A. de MIER ,
S. D. NOBLE  and
M. NOY
A. J. GOODALL
Affiliation:
Department of Applied Mathematics and Institute of Theoretical Computer Science, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic (e-mail: [email protected])
A. de MIER
Affiliation:
Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain (e-mail: [email protected], [email protected])
S. D. NOBLE
Affiliation:
Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge UB8 3PH, UK (e-mail: [email protected])
M. NOY
Affiliation:
Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain (e-mail: [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that if G is a simple outerplanar graph and H is a graph with the same Tutte polynomial as G, then H is also outerplanar. Examples show that the condition of G being simple cannot be omitted.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 4 , July 2011 , pp. 609 - 616
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bodirsky, M., Giménez, O., Kang, M. and Noy, M. (2007) Enumeration and limit laws for series-parallel graphs. Europ. J. Combin. 28 2091–2105.CrossRefGoogle Scholar
[2]Brylawski, T. H. (1971) A combinatorial model for series-parallel networks. Trans. Amer. Math. Soc. 154 1–22.Google Scholar
[3]Brylawski, T. H. (1972) A decomposition for combinatorial geometries. Trans. Amer. Math. Soc. 171 235–282.CrossRefGoogle Scholar
[4]Brylawski, T. and Oxley, J. (1992) The Tutte polynomial and its applications. In Matroid Applications (White, N., ed.), Vol. 40 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, pp. 123–225.CrossRefGoogle Scholar
[5]Chartrand, G. and Harary, F. (1967) Planar permutation graphs. Ann. Inst. H. Poincaré Sect. B (NS) 3 433–438.Google Scholar
[6]Dirac, G. A. (1952) A property of 4-chromatic graphs and some remarks on critical graphs. J. London Math. Soc. 27 85–92.CrossRefGoogle Scholar
[7]Eppstein, D. (1992) Parallel recognition of series-parallel graphs. Inform. Comput. 98 41–55.CrossRefGoogle Scholar
[8]Merino, C., de Mier, A. and Noy, M. (2001) Irreducibility of the Tutte polynomial of a connected matroid. J. Combin. Theory Ser. B 83 298–304.CrossRefGoogle Scholar
[9]de Mier, A. (2003) Graphs and matroids determined by their Tutte polynomials. PhD thesis, Universitat Politècnica de Catalunya.Google Scholar
[10]de Mier, A. and Noy, M. (2005) On matroids determined by their Tutte polynomials. Discrete Math. 302 52–76.CrossRefGoogle Scholar
[11]Schwärzler, W. (1991) Being Hamiltonian is not a Tutte invariant. Discrete Math. 91 87–89.CrossRefGoogle Scholar
[12]Whitney, H. (1932) Non-separable and planar graphs. Trans. Amer. Math. Soc. 34 339–362.CrossRefGoogle Scholar