Verification
Both the reconstruction and set reconstruction conjectures have been verified for all graphs with at most 11 vertices (McKay).
In a probabilistic sense, it has been shown (Bollobás) that almost all graphs are reconstructible. This means that the probability that a randomly chosen graph on vertices is not reconstructible goes to 0 as goes to infinity. In fact, it was shown that not only are almost all graphs reconstructible, but in fact that the entire deck is not necessary to reconstruct them — almost all graphs have the property that there exist three cards in their deck that uniquely determine the graph.
Read more about this topic: Reconstruction Conjecture
Famous quotes containing the word verification:
“Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements.”
—Rudolf Carnap (1891–1970)
“A fact is a proposition of which the verification by an appeal to the primary sources of our knowledge or to experience is direct and simple. A theory, on the other hand, if true, has all the characteristics of a fact except that its verification is possible only by indirect, remote, and difficult means.”
—Chauncey Wright (1830–1875)