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 … WebClose connections between percolation and random graphs, graph morphisms and hard-constraint models, and slow mixing and phase transition have led to new results and perspectives. These...

Counting Homomorphisms to Trees Modulo a Prime

Web2.1 Weighted graph homomorphisms A weighted graph His a graph with a positive real weight αH(i) associated with each node iand a real weight βH(i,j) associated with each edge ij. Let Gbe an unweighted graph (possibly with multiple edges, but no loops) and H, a weighted graph. To every homomorphism φ: V(G) → 2 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, … philosophers by era

Graph homomorphisms II: some examples

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 … WebWe show that for any finite, n-regular, bipartite graph G and any finite graph H (perhaps with loops), Hom(G, H) is maximum when G is a disjoint union of Kn,n’s. This generalizes a … 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... philosophers bowls of rice