Graphs and Combinatorics

, Volume 3, Issue 1, pp 45–53 | Cite as

The class reconstruction number of maximal planar graphs

  • Frank Harary
  • Josef Lauri
Article

Abstract

The reconstruction numberrn(G) of a graphG was introduced by Harary and Plantholt as the smallest number of vertex-deleted subgraphsG i =G − v i in the deck ofG which do not all appear in the deck of any other graph. For any graph theoretic propertyP, Harary defined theP-reconstruction number of a graph G ∈P as the smallest number of theG i in the deck ofG, which do not all appear in the deck of any other graph inP We now study the maximal planar graph reconstruction numberℳrn(G), proving that its value is either 1 or 2 and characterizing those with value 1.

Keywords

Planar Graph Graph Reconstruction Maximal Planar Graph Class Reconstruction Reconstruction Number 

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References

  1. 1.
    Chartrand, G., Kaugars, A., and Lick, D.R.: Criticallyn-connected graphs. Proc. Amer. Math. Soc.32, 63–68 (1972)Google Scholar
  2. 2.
    Fiorini, S., Lauri, J.: The reconstruction of maximal planar graphs. I. Recognition. J. Comb. Theory (B)30, 188–195 (1981)Google Scholar
  3. 3.
    Harary, F.: Graph Theory. Reading: Addison-Wesley 1969Google Scholar
  4. 4.
    Harary, F.: Conditional graph theory: Colorability, connectivity, reconstruction. Proc. First China-USA Conf. on Graph Theory (to appear)Google Scholar
  5. 5.
    Harary, F., Plantholt, M.: The graph reconstruction number. J. Graph Theory9, 451–454 (1985).Google Scholar
  6. 6.
    Lauri, J.: The reconstruction of maximal planar graphs. II. Reconstruction. J. Comb. Theory (B)30, 196–214 (1981)Google Scholar
  7. 7.
    Ore, O.: The Four-Color Problem. New York: Academic Press 1967Google Scholar
  8. 8.
    Whitney, H.: Congruent graphs and the connectivity of graphs. Amer. J. Math.54, 150–168 (1932)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Frank Harary
    • 1
  • Josef Lauri
    • 2
  1. 1.The University of MichiganAnn ArborUSA
  2. 2.The University of MaltaMsidaMalta

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