Labeling schemes for vertex connectivity

This article studies labeling schemes for the vertex connectivity function on general graphs. We consider the problem of assigning short labels to the nodes of any n-node graph is such a way that given the labels of any two nodes u and v, one can decide whether u and v are k-vertex connected in G, that is, whether there exist k vertex disjoint paths connecting u and v. This article establishes an upper bound of k²log n on the number of bits used in a label. The best previous upper bound for the label size of such a labeling scheme is 2^klog n.