Scaling relation for the critical exponents of the backbone of percolation clusters

The author suggests that beta B, the critical exponent of the backbone of percolation clusters, is given by beta B=1/2( gamma +5 beta )-1, where gamma and beta are susceptibility and order parameter exponents of percolation respectively. The proposed relation agrees with the epsilon expansion of beta B given by Harris and Lubensky and provides accurate estimates of beta B at all d>1. This relation may suggest that the backbone exponents are not independent of other percolation exponents. The author also suggests a more general relation for the order parameter exponent of m-connected clusters.