The Vertex Separation and Search Number of a Graph

  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.},
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
Highly Influential
This paper has highly influenced 13 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS


Publications citing this paper.
Showing 1-10 of 129 extracted citations


Publications referenced by this paper.
Showing 1-10 of 21 references

Pursuit-Evasion in a Graph’

  • T. D. Parsons
  • in Theory and Application of Graphs,
  • 1976
Highly Influential
6 Excerpts

The Search Number of a Connected Graph’

  • T. D. Parsons
  • Proc. 9th Southeastern Conf. on Combinatorics…
  • 1978
Highly Influential
2 Excerpts

Complexity of finding embeddings in a k -tree’

  • S. Arnborg, D. G. Corneil, A. Proskurowski
  • SIAM J. Alg. Disc. Meth.,
  • 1987

Similar Papers

Loading similar papers…