THE DOUBLE RECONSTRUCTION CONJECTURES ABOUT COLORED HYPERGRAPHS AND COLORED DIRECTED-GRAPHS

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 a : V --> V' and an integer m, k less-than-or-equal-to m less-than-or-equal-to n - k, such that for any k-subset W of V(G), G-W is isomorphic to G'-alpha(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 less-than-or-equal-to 1, are not doubly m-hypomorphic for any 2(n-2) + 1 less-than-or-equal-to m less-than-or-equal-to 3.2(n-2).