On the rooted Tutte polynomial

F. Y. Wu; C. King; W. T. Lu

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 3, page 1103-1114
  • ISSN: 0373-0956

Abstract

top
The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph.

How to cite

top

Wu, F. Y., King, C., and Lu, W. T.. "On the rooted Tutte polynomial." Annales de l'institut Fourier 49.3 (1999): 1103-1114. <http://eudml.org/doc/75359>.

@article{Wu1999,
abstract = {The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph.},
author = {Wu, F. Y., King, C., Lu, W. T.},
journal = {Annales de l'institut Fourier},
keywords = {graph colorings; the rooted Tutte polynomial; planar partitions; duality relation},
language = {eng},
number = {3},
pages = {1103-1114},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the rooted Tutte polynomial},
url = {http://eudml.org/doc/75359},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Wu, F. Y.
AU - King, C.
AU - Lu, W. T.
TI - On the rooted Tutte polynomial
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 3
SP - 1103
EP - 1114
AB - The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph.
LA - eng
KW - graph colorings; the rooted Tutte polynomial; planar partitions; duality relation
UR - http://eudml.org/doc/75359
ER -

References

top
  1. [1] G.D. BIRKHOFF, A determinant formula for the number of ways of coloring of a map, Ann. Math., 14 (1912), 42-46. Zbl43.0574.02JFM43.0574.02
  2. [2] W.T. TUTTE, A contribution to the theory of chromatic polynomials, Can. J. Math., 6 (1954), 80-91. Zbl0055.17101MR15,814c
  3. [3] W.T. TUTTE, On dichromatic polynomials, J. Comb. Theory, 2 (1967), 301-320. Zbl0147.42902MR36 #6320
  4. [4] W.T. TUTTE, Graph Theory, in Encyclopedia of Mathematics and Its Applications, Vol. 21, Addison-Wesley, Reading, Massachusetts, 1984, Chap. 9. Zbl0554.05001
  5. [5] H. WHITNEY, The coloring of graphs, Ann. Math., 33 (1932), 688-718. Zbl0005.31301JFM58.0606.01
  6. [6] See, for example, L.J. VAN LINT and R.M. WILSON, A course in combinatorics, Cambridge University Press, Cambridge, 1992, p. 301. Zbl0769.05001
  7. [7] H.N.V. TEMPERLEY and E.H. LIEB, Relations between the percolation and colouring problem and other graph-theoretical problems associated with regular planar lattice: some exact results for the percolation problem, Proc. Royal Soc. London A, 322 (1971), 251-280. Zbl0211.56703MR58 #16425
  8. [8] W.T. TUTTE, The matrix of chromatic joins, J. Comb. Theory B, 57 (1993), 269-288. Zbl0793.05030MR94a:05144
  9. [9] F.Y. WU and H.Y. HUANG, Sum rule identities and the duality relation for the Potts n-point boundary correlation function, Phys. Rev. Lett., 79 (1997), 4954-4957. Zbl0945.82002MR98h:82017
  10. [10] W.T. LU and F.Y. WU, On the duality relation for correlation functions of the Potts model, J. Phys. A: Math. Gen., 31 (1998), 2823-2836. Zbl0907.60081MR99d:82014
  11. [11] F.Y. WU, Duality relations for Potts correlation functions, Phys. Letters A, 228 (1997), 43-47. Zbl0962.82512MR97m:82003
  12. [12] See, for example, F.Y. WU, The Potts Model, Rev. Mod. Phys., 54 (1982), 235-268. 
  13. [13] R.B. POTTS, Some generalized order-disorder transformations, Proc. Camb. Philos. Soc., 48 (1954), 106-109. Zbl0048.45601MR13,896c
  14. [14] C.M. FORTUIN and P.W. KASTELEYN, On the random-cluster model I. Introduction and relation to other models, Physica, 57 (1972), 536-564. 
  15. [15] F.Y. WU and Y.K. WANG, Duality transformation in a many-component spin model, J. Math. Phys., 17 (1976), 439-440. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.