%0 Journal Article
%T Good edge-labelings and graphs with girth at least five
%A Michel Bode
%A Babak Farzad
%A Dirk Oliver Theis
%J Mathematics
%D 2011
%I arXiv
%X A good edge-labeling of a graph [Ara\'ujo, Cohen, Giroire, Havet, Discrete Appl. Math., forthcoming] is an assignment of numbers to the edges such that for no pair of vertices, there exist two non-decreasing paths. In this paper, we study edge-labeling on graphs with girth at least 5. In particular we verify, under this additional hypothesis, a conjecture by Ara\'ujo et al. This conjecture states that if the average degree of G is less than 3 and G is minimal without an edge-labeling, then G \in {C_3,K_{2,3}}. (For the case when the girth is 4, we give a counterexample.)
%U http://arxiv.org/abs/1109.1125v3