The 81 squares in the grid correspond to vertices in a mathematical graph ... Each vertex represents a different committee, and two committees are joined by a line if they have a member in ...

These graphs consist of collections of points ... the pentagon (or really any five-sided polygon), also called a five-cycle, and the five-vertex path, which consists of four line segments linked ...

as the measurement to decide which splittable vertex to decompose (see line 4 of Algorithm 1, below). We emphasize that if the splice graph contains a nontrivial vertex, then decomposing a trivial ...

the vertex is a maximum turning point We can identify these properties from a quadratics graph or equation.