β Scribed by Neal Madras
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π SIMILAR VOLUMES
The critical probability for site percolation on the square lattice is not known exactly. Several authors have given rigorous upper and lower bounds. Some recent lower bounds are (each displayed here with the first three digits) 0.503 (Toth [13]), 0.522 (Zuev [15]), and the best lower bound so far,
If a graph G with cycle rank p contains both spanning trees with rn and with n end-vertices, rn < n, then G has at least 2p spanning trees with k end-vertices for each integer k, rn < k < n. Moreover, the lower bound of 2p is best possible. [ l ] and Schuster [4] independently proved that such span
In 1968, Vizing conjectured that if G is a -critical graph with n vertices, then (G) β€ n / 2, where (G) is the independence number of G. In this paper, we apply Vizing and Vizing-like adjacency lemmas to this problem and prove that (G)<(((5 -6)n) / (8 -6))<5n / 8 if β₯ 6. α§ 2010 Wiley
By using a fl-function for a spin -3 Ising model, we investigate the critical phenomena of a general two-layer Ising model of square lattice. We find that the value of the shift exponent ~b is 1.73 ~ 0.04 for the system with the same intra-layer interaction and 0.5 for the system with different intr
## Abstract The upper bound for the harmonious chromatic number of a graph that has been given by SinβMin Lee and John Mitchem is improved.