Abstract
This paper introduces two new reconstruction conjectures about colored hypergraphs and colored directed graphs, and presents results about these two conjectures some of which are as follows: (1) the restricted version of the first conjecture to simple graphs is equivalent to the Ulam's Conjecture; (2) Kokay's each hypomorphic pair (X n ,Y n ), n=2,3,..., of 3-hypergraphs does not satisfy the conditions in the first conjecture; (3) any two (0, k)-hypergraphs G and G′ of order n are isomorphic if there exists a bijection α: V→V′ and an integer m, k ≤ m ≤ n-k, such that for any k-subset W of V(G), G- W is isomorphic to G′- α(W); (4) the validity of the second conjecture implies the validity of the Ulam's Conjecture; (5) Stockmeyer's hypomorphic tournaments, B n and C n , n ≤ 1, are not doubly m-hypomorphic for any 2n−2+1≤m≤ 3 · 2n−2.
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© 1992 Springer-Verlag Berlin Heidelberg
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Hashiguchi, K. (1992). The double reconstruction conjectures about colored hypergraphs and colored directed graphs. In: Simon, I. (eds) LATIN '92. LATIN 1992. Lecture Notes in Computer Science, vol 583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023833
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DOI: https://doi.org/10.1007/BFb0023833
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