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## 13.3 Treelike Equalities and Euler-Type Inequalities

In this section we present treelike equalities and Euler type inequalities for median graphs and their generalizations: quasi-median graphs, partial cubes, and cage-amalgamation graphs.

### 13.3.1 Treelike Eequalities and Euler-Type Inequalities for Median Graphs

Let G be a median graph. Two splits{A, } and {B, } of G are said to be incompatible if all four of the possible intersections AB, A, B, and are nonempty (otherwise they are called compatible). The corresponding Θ-classes FA and FB are said to cross if the splits{A, } and {B, } are incompatible. The next theorem, probably observed for the first time by Isbell [44] (in slightly different ...

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