The minimal book embedding conjecture for graphs

Let $G$ be a graph, and let $mnl(G)$ denote the minimum number of links among spatial embeddings of $G$. A book embedding is a spatial embedding in which the graph is embedded with respect to a book structure, and a minimal book embedding is one having the minimum number of links among book embeddings of $G$. Minimal book embedding conjecture. For any graph $G$, there is a minimal book embedding of $G$ which realizes

$$mnl(G).$$

The conjecture is suggested by computations for canonical book representations of complete graphs, including the example for $K_8$. It asserts that the global minimum number of links is always attained by a book embedding; the general claim remains open.