Anti-magic graphs via the combinatorial NullStellenSatz

An antimagic labeling of a graph with m edges and n vertices is a bijection from the set of edges to the integers 1,..., m such that all n vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with that vertex. A graph is called antimagic if it has an antimagic labeling. In [10], Ringel conjectured that every simple connected graph, other than K₂, is antimagic. We prove several special cases and variants of this conjecture. Our main tool is the Combinatorial NullStellenSatz (Cf. [1]).