A note on fragments of infinite graphs

Given a g raph At, let x= denote the least card ina l i ty o f a vertex set which separa tes two infinite subsets of the ver tex set V(X) of X. In this note graphs X with finite ~= are considered. I f S separa tes the infinite sets C1, C~ where IS[ = z = and V(X) = Ca U S U Cz, then C1, C2 are called fragments of X. L. Babai and M. E. Wa tk in s [1] showed… (More)