Abstract#R##N##R##N#We consider the following graph labeling problem, introduced by Leung et al. (J. Y-T. Leung, O. Vornberger, and J. D. Witthoff, On some variants of the bandwidth minimization problem. SIAM J. Comput. 13 (1984) 650–667). Let G be a graph of order n, and f a bijection from V(G) to the integers 1 through n. Let |f|, and define s(G), the separation number of G, to be the maximum of |f| among all such bijections f. We first derive some basic relations between s(G) and other graph parameters. Using a general strategy for analyzing separation number in bipartite graphs, we obtain exact values for certain classes of forests and asymptotically optimal lower bounds for grids and hypercubes.
['Zevi Miller', 'Dan Pritikin']
On the separation number of a graph