Distinguishing graphs by their left and right homomorphism profiles

European Journal of Combinatorics

Volumn 32, Issue 7, 2011, Pages 1025-1053

  Garijo, Delia ^a   Goodall, Andrew ^b   Nesetril Jaroslav J ^b  

^a UNIVERSITY OF SEVILLE   (Spain)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79961005858     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejc.2011.03.012     Document Type: Article

References (37)

1. Alon N., Tarsi M. Colorings and orientations of graphs. Combinatorica 1992, 12:125-134.
2. Andrén D., Markström K. The bivariate Ising polynomial of a graph. Discrete Appl. Math. 2009, 157(11):2515-2524.
3. Averbouch I., Godlin B., Makowsky J. An extension of the bivariate chromatic polynomial. European J. Combin. 2010, 31:1-17.
4. Biggs N. Algebraic Graph Theory 1994, Cambridge Univ. Press, Cambridge. 2nd ed.
5. Bollobás B. Modern Graph Theory. Grad. Texts in Math 1998, Springer, New York.
6. Bollobás B., Pebody L., Riordan O. Contraction-deletion invariants for graphs. J. Combin. Theory Ser. B 2000, 80:320-345.
7. Bollobás B., Riordan O. A Tutte polynomial for coloured graphs. Combin. Probab. Comput. 1999, 8:45-94.
8. Borgs C., Chayes J., Lovász L., Sós V., Vesztergombi K. Counting graph homomorphisms. Topics in Discrete Mathematics 2007, 315-371. Springer, New York. M. Klazar, J. Kratochvíl, M. Loebl, J. MatouŠek, R. Thomas, P. Valtr (Eds.).
9. Brylawski T., Oxley J. The Tutte polynomial and its applications. Encyclopedia Math. Appl. 1992, vol. 40:123-225. Cambridge Univ. Press, Cambridge. N. White (Ed.).
10. Chen X.E., Bao X.W., Ouyang K.Z. Chromaticity of the graph θ(a,b,c,d). J. Shanxi Normal Univ. 1992, 20:75-79. (in Chinese) English summary.
11. de Mier A., Noy M. On graphs determined by their Tutte polynomial. Graphs Combin. 2004, 20:105-119.
12. Dohmen K., Pönitz A., Tittmann P. A new two-variable generalization of the chromatic polynomial. Discrete Math. Theor. Comput. Sci. 2003, 6:69-90.
13. Duan Y., Wu H., Yu Q. On chromatic and flow polynomial unique graphs. Discrete Appl. Math. 2008, 156(12):2300-2309.
14. Z. Dvořák, On recognizing graphs by numbers of homomorphisms, Tech. Rep. 2006-287, ITI, Charles University, Prague, 2006.
15. Dyer M., Greenhill C. The complexity of counting graph homomorphisms. Random Structures Algorithms 2000, 17:260-289.
16. Freedman M., Lovász L., Schrijver A. Reflection positivity, rank connectivity, and homomorphisms of graphs. J. Amer. Math. Soc. 2007, 20:37-51.
17. Garijo D., Goodall A., Nešetřil J. Graph homomorphisms, the Tutte polynomial and q-state Potts uniqueness. Electron. Notes Discrete Math. 2009, 34:231-236.
18. Garijo D., Márquez A., Revuelta M. Tutte uniqueness of locally grid graphs. Ars Combin. 2009, 92:377-396.
19. Garijo D., Nešetřil J., Revuelta M. Homomorphisms and polynomial invariants of graphs. European J. Combin. 2009, 30:1659-1675.
20. Godsil C., Royle G. Algebraic Graph Theory. Grad. Texts in Math. 2001, Springer, New York.
21. Goodall A. Fourier analysis on finite Abelian groups: some graphical applications. Oxford Lecture Ser. Math. Appl. 2007, vol. 34:103-129. Oxford Univ. Press, Oxford, (Chapter 7). G. Grimmett, C. McDiarmid (Eds.).
22. Gutman I., Harary F. Generalizations of the matching polynomial. Util. Math. 1983, 24:97-106.
23. Hell P., Nešetřil J. Graphs and Homomorphisms. Oxford Lecture Ser. Math. Appl. 2004, 28. Oxford Univ. Press, Oxford.
24. Koh K., Teo K. The search for chromatically unique graphs. Graphs Combin. 1990, 6:259-285.
25. Koh K., Teo K. The search for chromatically unique graphs-II. Discrete Math. 1997, 172:59-78.
26. Lovász L. Operations with structures. Acta Math. Hungar. 1967, 18:321-328.
27. Lovász L. The rank of connection matrices and the dimension of graph algebras. European J. Combin. 2006, 27:962-970.
28. Lovász L., Schrijver A. Dual graph homomorphism functions. J. Combin. Theory Ser. A 2010, 117:216-222.
29. Márquez A., de Mier A., Noy M., Revuelta M.P. Locally grid graphs: classification and Tutte uniqueness. Discrete Math. 2003, 266(1-3):327-352.
30. Noy M. Graphs determined by polynomial invariants. Theoret. Comput. Sci. 2003, 307(2):365-384.
31. Read R., Whitehead E.W. A note on chain lengths and the Tutte polynomial. Discrete Math. 2008, 308(10):1826-1829.
32. Schwenk A. Almost all trees are cospectral. New Directions in the Theory of Graphs 1973, 275-307. Academic Press, New York. F. Harary (Ed.).
33. P. Tittmann, I. Averbouch, J. Makowsky, The enumeration of vertex induced subgraphs with respect to the number of components, 2009. [math.CO]. arxiv:0812.4147.
34. Tutte W.T. A class of Abelian groups. Canad. J. Math. 1956, 8:13-28.
35. van Dam E.R., Haemers W.H. Which graphs are determined by their spectrum?. Linear Algebra Appl. 2003, 373:241-272.
36. Welsh D. Complexity: Knots, Colourings and Counting. London Math. Soc. Lect. Notes Ser. 1993, Cambridge Univ. Press, Cambridge.
37. Widom B., Rowlinson J.S. New model for the study of liquid-vapour phase transition. J. Chem. Phys. 1970, 52:1670-1684.