Skip to main content

On the hamiltonian completion problem

Part III: Contributed Papers New Results On Graphs And Combinatorics

Part of the Lecture Notes in Mathematics book series (LNM,volume 406)

Abstract

We define the Hamiltonian completion number of a graph G, denoted hc(G), to be the minimum number of lines that need to be added to G in order to make it Hamiltonian. The Hamiltonian completion problem asks for hc(G) and a specific Hamiltonian cycle containing hc(G) new lines. We derive an efficient algorithm for finding hc(T) for any tree T, and show that if S is the set of spanning trees of an arbitrary connected graph G, then

.

A number of other general results are presented including an efficient heuristic procedure which can be used on arbitrary graphs.

Keywords

  • Span Tree
  • Connected Graph
  • Travel Salesman Problem
  • Hamiltonian Cycle
  • Hamiltonian Path

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Karp, R. M., "Reducibility Among Combinatorial Problems," Complexity of Computer Computations (R. Miller and J. Thatcher, Eds.)

    Google Scholar 

  2. Harary, F., and Schwenk, A., "Evolution of the Path Number of a Graph, Covering and Packing in Graphs, II," Graph Theory and Computing (R.C. Read, ed.) Academic Press, New York, 1972, 39–45.

    Google Scholar 

  3. Boesch, F. T., Chen, S., and McHugh, N.A.M., "On Covering the Points of a Graph with Point Disjoint Paths," this volume p. 201.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1974 Springer-Verlag Berlin

About this paper

Cite this paper

Goodman, S., Hedetniemi, S. (1974). On the hamiltonian completion problem. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066448

Download citation

  • DOI: https://doi.org/10.1007/BFb0066448

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06854-9

  • Online ISBN: 978-3-540-37809-9

  • eBook Packages: Springer Book Archive