WebWe provide an upper bound to the number of graph homomorphisms from to , where is a fixed graph with certain properties, and varies over all -vertex, -regular graphs. This result generalizes a recently resolved conjecture of Alon and Kahn on the number of independent sets. We build on the work of Galvin and Tetali, who studied the number of graph … Web1 de set. de 2024 · Our theorem applies to all non-negative weighted forms of the problem: given any fixed matrix A with non-negative algebraic entries, the partition function ZA (G) of directed graph...
Edge-reflection positivity and weighted graph homomorphisms
Web1 de abr. de 2016 · The number of homomorphisms from a finite graph F to the complete graph K n is the evaluation of the chromatic polynomial of F at n.Suitably scaled, this is the Tutte polynomial evaluation T (F; 1 − n, 0) and an invariant of the cycle matroid of F.De la Harpe and Jaeger asked more generally when is it the case that a graph parameter … Web13 de abr. de 2006 · 2.4. Connection matrices of homomorphisms. Fix a weighted graph H = (a,B). For every positive integer k,let[k]={1,...,k}. For any k-labeled graph G and … on sharp 意味
Homomorphisms of signed graphs: An update
Web26 de fev. de 2013 · Using some results in geometric invariant theory, we characterize for which weighted graphs the edge-coloring model can be taken to be real valued that is, … WebGiven an edge-weighted graph(G,w), denote by mcH(G,w) the measure of the optimal solution to the problem MAX H-COL.Denote by mck(G,w) the (weighted) size of a largest k-cut in(G,w). This notation is justified by the fact that mck(G,w) = mcK k (G,w). In this sense, MAX H-COL generalises MAX k-CUT which is a well-known and well-studied problem … Web1 de ago. de 2009 · 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, Lovász and... ons hart