3 research outputs found
Graph homomorphisms, the Tutte polynomial and “q-state Potts uniqueness”
We establish for which weighted graphs H homomorphism functions from multigraphs
G to H are specializations of the Tutte polynomial of G, answering a question
of Freedman, Lov´asz and Schrijver.
We introduce a new property of graphs called “q-state Potts uniqueness” and relate
it to chromatic and Tutte uniqueness, and also to “chromatic–flow uniqueness”,
recently studied by Duan, Wu and Yu.Ministerio de Educación y Ciencia MTM2005-08441-C02-0
Distinguishing graphs by their left and right homomorphism profiles
We introduce a new property of graphs called ‘q-state Potts unique-ness’ and relate it to chromatic and Tutte
uniqueness, and also to ‘chromatic–flow uniqueness’, recently studied by Duan, Wu and Yu.
We establish for which edge-weighted graphs H homomor-phism functions from multigraphs G to H are
specializations of the Tutte polynomial of G, in particular answering a question of Freed-man, Lovász and
Schrijver. We also determine for which edge-weighted graphs H homomorphism functions from
multigraphs G to H are specializations of the ‘edge elimination polynomial’ of Averbouch, Godlin and
Makowsky and the ‘induced subgraph poly-nomial’ of Tittmann, Averbouch and Makowsky.
Unifying the study of these and related problems is the notion of the left and right homomorphism profiles
of a graph.Ministerio de Educación y Ciencia MTM2008-05866-C03-01Junta de Andalucía FQM- 0164Junta de Andalucía P06-FQM-0164