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A note on the edge reconstruction conjecture

Published online by Cambridge University Press:  17 April 2009

E.F. Schmeichel
E.F. Schmeichel
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, California, USA
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Abstract

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Let G be a graph with vertex degree sequence d1 ≤ d2 ≤ … ≤ dp It is shown that if di + dp–i+1 ≥ p for some i, then G is uniquely reconstructable from its collection of maximal (edge deleted) subgraphs. This generalizes considerably a result of Lovász. As a corollary, it is shown that Chvátal's existence condition for hamiltonian cycles implies edge reconstructability as well.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1975 , pp. 27 - 30
Copyright
Copyright © Australian Mathematical Society 1975

References

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