The Vertex Separation and Search Number of a Graph

@article{Ellis1994TheVS,
title={The Vertex Separation and Search Number of a Graph},
author={John A. Ellis and Ivan Hal Sudborough and Jonathan S. Turner},
journal={Inf. Comput.},
year={1994},
volume={113},
pages={50-79}
}

We relate two concepts in graph theory and algorithmic complexity, namely the search number and the vertex separation of a graph. Let s (G ) denote the search number and vs (G ) denote the vertex separation of a connected, undirected graph G . We show that vs (G ) ≤ s (G ) ≤ vs (G ) +2 and we give a simple transformation from G to G ′ such that vs (G ′) = s (G ). We characterize those trees having a given vertex separation and describe the smallest such trees. We also note that there exist… CONTINUE READING