Dense graphs and edge reconstruction

Abstract

By a well-known result of Nash-Williams if a graphG is not edge reconstructible, then for all\(A \subseteq E(G)\),|A|≡|E(G)| mod 2 we have a permutation ϕ ofV(G) such thatE(G)∩E(Gϕ)=A. Here we construct infinitely many graphsG having this curious property and more than\(|G|\left[ {\sqrt {\log |G|} /2} \right]\) edges.

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Research (partially) supported by Hungarian National Foundation for Scientific Research Grant No.T016389.

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Pyber, L. Dense graphs and edge reconstruction. Combinatorica 16, 521–525 (1996). https://doi.org/10.1007/BF01271270

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Mathematics Subject Classification (1991)

  • 05 C 60