WebJ.-Y. Cai and X. Chen, A decidable dichotomy theorem on directed graph homomorphisms with nonnegative weights, in Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science, 2010, pp. 437--446. Google Scholar 6. Web16 de dez. de 2024 · Suppose F is simple graph and G is a weighted graph with β i j is the weight of i j edge in G. Now we define, h o m ϕ ( F, G) = ∏ i j ∈ E ( F) β ϕ ( i) ϕ ( j) and the homomorphism number is defined as h o m ( F, G) = ∑ ϕ: V ( F) → V ( G) h o m ϕ ( F, G)
Edge-reflection positivity and weighted graph homomorphisms
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... WebAs an important interim result, our study yields a dichotomy for the problem of counting weighted independent sets in a bipartite graph modulo some prime p. These results are the first suggesting that such dichotomies hold not only for the modulo 2 case but also for the modular counting functions of all primes p . play online games car
Spectral preorder and perturbations of discrete weighted graphs
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