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
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References

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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

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