We give below a description of the pictures we use to provide information on branch-and-cut runs.

Each node in the picture represents a subproblem in the branch-and-cut process. The two children of a node correspond to the two subproblems created when we carry out a branching step after applying cutting planes (for example, we might chose an edge between two cities and split the remaining tours into those that definitely use the edge and those that definitely do not use the edge).

The height of a node corresponds to the linear programming (LP) lower bound given by applying the cutting-plane method to the subproblem.

The active nodes are either red or magenta. The red nodes are those that have not yet gone through additional rounds of the cutting-plane procedure after the branching step (the subproblems retain the cutting planes that were found for their parent, but no additional cuts have yet been generated).