2017/08/08 by Lozano, Antoni
#05C05 #05C78 #68R10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1708.02607
An antimagic labeling of a directed graph D with m arcs is a bijection from the set of arcs of D to \1,…,m\ such that all oriented vertex sums of vertices in D are pairwise distinct, where the oriented vertex sum of a vertex u is the sum of labels of all arcs entering u minus the sum of labels of all arcs leaving u. Hefetz, Mütze, and Schwartz conjectured that every connected graph admits an antimagic orientation, where an antimagic orientation of a graph G is an orientation of G which has an antimagic labeling. We use a constructive technique to prove that caterpillars, a well-known subclass of trees, have antimagic orientations.