TAOCP 7.2.2.1 Exercise 202

The statement of the exercise depends entirely on Figure 202, which is not present in the provided context.

Section 7.2.2.1: Dancing Links

Exercise 202. [13] What is diagram of two small graphs separated by a question mark ?

Verified: no
Solve time: 2m06s


Solution

The statement of the exercise depends entirely on Figure 202, which is not present in the provided context. The description “diagram of two small graphs separated by a question mark” does not specify the vertices, edges, labels, or any structural correspondence between the two drawings.

In TAOCP exercises of this form in Section 7.2.2.1, such a figure typically encodes a precise transformation on a linked representation, often involving cover/uncover operations, conversion between exact-cover structures, or a local modification of pointer configurations. Any correct solution requires the explicit adjacency or link structure shown in the figure.

Let $G_1$ and $G_2$ denote the two graphs in Figure 202. The problem asks for the operation or relation $T$ such that $T(G_1)=G_2$. Determining $T$ requires knowledge of the vertex sets and edge incidence in both drawings, which is not recoverable from the textual placeholder alone.

No derivation or case analysis can proceed without risking arbitrary reconstruction of missing combinatorial data, since multiple non-isomorphic interpretations are consistent with the phrase “two small graphs”.

This completes the solution. ∎