Routing and wavelength assignment in all-optical networks
IEEE/ACM Transactions on Networking (TON)
New asymptotics for bipartite Tura´n numbers
Journal of Combinatorial Theory Series A
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of the matching-cut problem for planar graphs and other graph classes
Journal of Graph Theory
Directed acyclic graphs with the unique dipath property
Theoretical Computer Science
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A good edge-labelling of a graph G is a labelling of its edges such that, for any ordered pair of vertices (x,y), there do not exist two paths from x to y with increasing labels. This notion was introduced by Bermond et al. (2009) [2] to solve wavelength assignment problems for specific categories of graphs. In this paper, we aim at characterizing the class of graphs that admit a good edge-labelling. First, we exhibit infinite families of graphs for which no such edge-labelling can be found. We then show that deciding whether a graph G admits a good edge-labelling is NP-complete, even if G is bipartite. Finally, we give large classes of graphs admitting a good edge-labelling: C"3-free outerplanar graphs, planar graphs of girth at least 6, {C"3,K"2","3}-free subcubic graphs and {C"3,K"2","3}-free ABC-graphs.