Finding structure in sequences of real numbers via graph theory: a problem list

We investigate a method of generating a graph G = (V, E) out of an ordered list of n distinct real numbers a(1),..., a(n). These graphs can be used to test for the presence of combinatorial structure in the sequence. We describe sequences exhibiting intricate hidden structure that was discovered this way. Our list includes sequences of Deutsch, Erd.os, Freud and Hegyvari, Recaman, Quet, Zabolotskiy and Zizka. Since our observations are mostly empirical, each sequence in the list is an open problem.