Let X → Y be a Galois covering of curves, where the genus of X is ≥ 2 and the genus of Y is ≤ 2. We prove that under certain hypotheses, X has an unramified cover that dominates a hyperelliptic curve; our results apply, for instance, to all tamely superelliptic curves. Combining this with a theorem of Bogomolov and Tschinkel shows that X has an unramified cover that dominates y = x − 1, if char...

In this paper, some earlier results by Fleischner [H. Fleischner, Bipartizing matchings and Sabidussi’s compatibility conjecture, DiscreteMath. 244 (2002) 77–82] about edge-disjoint bipartizingmatchings of a cubic graphwith a dominating circuit are generalized for graphs without the assumption of the existence of a dominating circuit and 3-regularity. A pair of integer flows (D, f1) and (D, f2)...