 If formula_5 is this 2-regular graph and has formula_6 vertices, the question is whether the complete graph formula_7 can be represented as an edge-disjoint union of copies of formula_5.In order for a solution to exist, the total number of conference participants (or equivalently, the total capacity of the tables, or the total number of vertices of the given cycle graphs) must be an odd number.For, at each meal, each participant sits next to two neighbors, so the total number of neighbors of each participant must be even, and this is only possible when the total number of participants is odd.