Good edge-labelings and graphs with girth at least five

Details Good edge-labelings and graphs with girth at least five Good edge-labelings and graphs with girth at least five

2011-09-06

arxiv.org/abs/1109.1125v2

Mathematics

Combinatorics

22 pages + appendix

Scientific paper

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 graph graphs with girth at least five. 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 is either C_3 or K_{2,3}.

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