×

Reconstructing graphs from their k-edge deleted subgraphs. (English) Zbl 0595.05050

Let G be a graph with m edges and n vertices. We show that if \(2^{m- k}>n!\) or if \(2m>\left( \begin{matrix} n\\ 2\end{matrix} \right)+k\) then G is determined by its collection of k-edge deleted subgraphs.

MSC:

05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bondy, J. A.; Hemminger, R. L., Graph reconstruction—A survey, J. Graph Theory, 1, 227-268 (1977) · Zbl 0375.05040
[2] Frankl, P.; Pach, J., On the number of sets in a null \(t\)-design, Europ. J. Combin., 4, 21-23 (1983) · Zbl 0508.05018
[3] Graham, R. L.; Li, S-Y. R.; Li, W-C. W., On the structure of \(t\)-designs, SIAM J. Algebra Discrete Math., 1, 8-14 (1980) · Zbl 0499.05012
[4] Harary, F., On the reconstruction of a graph from a collection of subgraphs, (Fiedler, M., Theory of Graphs and Its Applications (1964), Czechoslovak Academy of Sciences: Czechoslovak Academy of Sciences Prague), 47-52
[5] I. Krasikov and Y. Roditty; I. Krasikov and Y. Roditty · Zbl 0594.05049
[6] Lovász, L., A note on the line reconstruction problem, J. Combin. Theory Ser. B, 13, 309-310 (1972) · Zbl 0244.05112
[7] Müller, V., The edge reconstruction conjecture is true for graphs with more than \(n log_2n\) edges, J. Combinatorial Theory Ser. B, 22, 281-283 (1977) · Zbl 0344.05161
[8] Stanley, R. P., Quotients of Peck posets, Order, 1, 29-34 (1984) · Zbl 0564.06002
[9] Stanley, R. P., Reconstruction from vertex switching, J. Combin. Theory Ser. B, 38, 132-138 (1985) · Zbl 0572.05046
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.