"194894" . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . . "P(1M0545), Z(MSM0021620838)" . "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. We establish for which edge-weighted graphs H homomorphism functions from multigraphs G to H are specializations of the Tutte polynomial of G, in particular answering a question of Freedman, Lovasz 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 polynomial'' 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."@en . . . "[51E150DAA303]" . "Garijo, Delia" . "Goodall, Andrew" . . "European Journal of Combinatorics" . "29"^^ . . . "11320" . "32" . "0195-6698" . "7" . . "http://dx.doi.org/10.1016/j.ejc.2011.03.012" . "1"^^ . . "3"^^ . "Distinguishing graphs by their left and right homomorphism profiles" . "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. We establish for which edge-weighted graphs H homomorphism functions from multigraphs G to H are specializations of the Tutte polynomial of G, in particular answering a question of Freedman, Lovasz 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 polynomial'' 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." . "RIV/00216208:11320/11:10104595!RIV12-MSM-11320___" . . . "Distinguishing graphs by their left and right homomorphism profiles" . . . . "INVARIANTS; TUTTE UNIQUENESS; Potts uniqueness; homomorphism; CHROMATICALLY UNIQUE GRAPHS"@en . . . . "Distinguishing graphs by their left and right homomorphism profiles"@en . . "Distinguishing graphs by their left and right homomorphism profiles"@en . "000294580100007" . . "RIV/00216208:11320/11:10104595" . "10.1016/j.ejc.2011.03.012" . "Ne\u0161et\u0159il, Jaroslav" .