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Computer based proofs by induction in graph theory- a house of cards?

  • New Mexico Institute of Mining and Technology
  • University of New Mexico

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The role of computer generated data as an essential component of a mathematical proof is discussed. Some examples are given of graph theorems whose proofs share certain unusual features. These theorems are proven by induction on the order n of the graph with the inductive step frequently being easy. However, the theorems are not true for small values of n so that the base for the induction argument is established by large scale computation. We suggest that such computer based proofs will become commonplace and raise the question of what supporting evidence of correctness should be presented along with the computer generated data.

Original languageEnglish
Pages (from-to)17-23
Number of pages7
JournalMathematical and Computer Modelling
Volume17
Issue number11
DOIs
StatePublished - Jun 1993

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