In the dual graph, some constraints may be unnecessary. Indeed, dual constraints enforces equality of original variables., Someand edgessome constraints may be redundant because of transitivity of equality. For example, if <math>C_2</math> and <math>C_1</math> are joined by an edge whose label contains <math>y</math>, and so are <math>C_1</math> and <math>C_3</math>, equality of <math>y</math> in all three dual variables is guaranteed. As a result, a dual constraint between <math>C_2</math> and <math>C_3</math> enforcing equality of <math>y</math> is not necessary, and could be removed if present.
For example, if <math>C_2</math> and <math>C_1</math> are joined by an edge whose label contains <math>y</math>, and so are <math>C_1</math> and <math>C_3</math>, equality of <math>y</math> in all three dual variables is enforced. As a result, a dual constraint between <math>C_2</math> and <math>C_3</math> enforcing equality of <math>y</math> is not necessary.
