Labeling Schemes for Vertex Connectivity [chapter]

Amos Korman
Lecture Notes in Computer Science  
This paper 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, i.e., whether there exist k vertex disjoint paths connecting u and v. The paper establishes an upper bound of k 2 log 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 k log n.
doi:10.1007/978-3-540-73420-8_11 fatcat:5qovxlwmgjd3zlyrs7sf5pbqeu