LYNGSIE , Kasper

Horňak, Przybyło and Woźniak recently proved that, a small class of obvious exceptions apart, every digraph can be 4-arc-weighted so that, for every arc u->v, the sum of weights incoming to u is different from the sum of weights outgoing from v. They conjectured a stronger result, namely that the same statement with 3 instead of 4 should also...

For any S⊂ℤ we say that a graph G has the S-property if there exists an S-edge-weighting w:E(G)→S such that for any pair of adjacent vertices u,v we have Σ_{e∈E(v)} w(e) ≠ Σ_{e∈E(u)} w(e), where E(v) and E(u) are the sets of edges incident to v and u respectively. This work focuses on {a,a+2}-edge-weightings where a∈ℤ is odd. We show that a...