Good edgelabelings and graphs with girth at least five
Abstract
A good edgelabeling of a graph [Araújo, 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 nondecreasing paths. In this paper, we study edgelabeling on graphs with girth at least 5. In particular we verify, under this additional hypothesis, a conjecture by Araújo et al. This conjecture states that if the average degree of G is less than 3 and G is minimal without an edgelabeling, then G \in {C_3,K_{2,3}}. (For the case when the girth is 4, we give a counterexample.)
 Publication:

arXiv eprints
 Pub Date:
 September 2011
 DOI:
 10.48550/arXiv.1109.1125
 arXiv:
 arXiv:1109.1125
 Bibcode:
 2011arXiv1109.1125B
 Keywords:

 Mathematics  Combinatorics;
 05C78
 EPrint:
 23 pages + appendix