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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References
J. A. Bondy: A graph reconstructor's Manual, in Surveys in Combinatorics 1991, LMS, Lecture Note Series 166 (ed. A. Keedwell) Cambridge Univ. Press, 221–252.
C. R. J. Clapham, andJ. Sheehan: Super-free graphs,Ars Combinatoria,33 (1992), 245–257.
M. N. Ellingham, L. Pyber, andX. Yu: Claw-free graphs are edge reconstructible,J. Graph Theory,12 (1988), 445–451.
I. Krasikov: A note on the edge reconstruction ofK 1,m free graphs,JCT (B),49 (1990), 295–298.
L. Lovász: A note on the line reconstruction problem,JCT (B),13 (1972), 309–310.
V. Müller: The edge reconstruction hypothesis is true for graphs with more thann logn edges,JCT (B),22 (1977), 281–283.
C. St. J. A. Nash-Williams:The reconstruction problem in: Selected topics in graph theory, (1978) (eds. L. W. Beineke and R. J. Wilson) Acad. Press, 205–236.
L. Pyber: The edge reconstruction of Hamiltonian graphs,J. Graph Theory,14 (1990), 173–179.
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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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DOI: https://doi.org/10.1007/BF01271270