On the maximum number of pairwise compatible euler cycles

B. Jackson [4] made the following conjecture: If G is an Eulerian graph with δ(G) ≥ 2k, then G has a set of 2k - 2 pairwise compatible Euler cycles (i.e., every pair of adjacent edges appears in at most one of these Euler cycles as a pair of consecutive edges). We verify this conjecture in the case where every circuit of G is a block of G.