Abstract
We study the following problem: given a collection H=(Hi‖1≤i≤n) of n graphs, each on n-1 vertices, when does there exist a graph G whose vertex-deleted subgraphs are the members of H?
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References
J.A. Bondy and R.L. Hemminger, "Graph reconstruction — a survey", J. Graph Theory 1(1977), to appear.
J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, MacMillan, London and American Elsevier, New York, 1976.
J. Dénes and A.D. Keedwell, Latin Squares and their Applications, Academic Press, New York, 1974.
A.W. Goodman, "On sets of acquaintances and strangers at any party", Amer. Math. Monthly 66(1959), 778–783.
U. Hafstrøm, personal communication, 1976.
F. Harary, "On the reconstruction of a graph from a collection of subgraphs", in, Theory of Graphs and its Applications, (Proceedings of the Symposium held in Prague, 1964), edited by M. Fielder, Czechoslovak Academy of Sciences, Prague, 1964, 47–52.
F. Harary, "The four color conjecture and other graphical diseases", in Proof Techniques in Graph Theory, (Proceedings of the Second Ann Arbor Graph Theory Conference, Ann Arbor, Mich., 1968), edited by F. Harary, Academic Press, New York, 1969, 1–9.
W. Jackson, "Legitimate decks", preprint, 1977.
P.J. Kelly, "A congruence theorem for trees", Pacific J. Math. 7(1957), 961–968.
B. Manvel, "On reconstruction of graphs", in The Many Facets of Graph Theory, (Proceedings of the Conference held at Western Michigan University, Kalamazoo, Mich., 1968), edited by G. Chartrand and S.F. Kapoor, Lecture Notes in Math., Vol. 110, Springer-Verlag, New York, 207–214.
B. Manvel, "On reconstructing graphs from their sets of subgraphs", J. Combinatorial Theory (B), 21(1976), 156–165.
B.D. McKay, "Computer reconstruction of small graphs", J. Graph Theory 1(1977), to appear.
S. Ramachandran, "A test for legitimate decks", preprint, 1977.
M. Randić, "On the reconstruction problem for graphs", preprint, 1977.
J.E. Simpson, "Legitimate decks of graphs", Notices Amer. Math. Soc. 21(1974), A-39.
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© 1978 Springer-Verlag
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Bondy, J.A. (1978). Reflections on the legitimate deck problem. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062511
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DOI: https://doi.org/10.1007/BFb0062511
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