Labeling schemes for vertex connectivity

Abstract

This paper studies labeling schemes for the vertex connectivity function on general graphs. We consider the problem of labeling the nodes of any n-node graph is such a way that given the labels of two nodes u and v, one can decide whether u and v are k-vertex connected in G, i.e., whether there exist k vertex disjoint paths connecting u and v. The paper establishes an upper bound of l2log n on the number of bits used in a label. The best previous upper bound for the label size of such labeling scheme is 2k log n. © Springer-Verlag Berlin Heidelberg 2007.