Case 1: The three close pairs share a common vertex — e.g., a star of 3 edges: \( AB, AC, AD \). But we only have 3 edges — this uses all 3 close pairs incident to A. Then consider trio \( B,C,D \): no edges among them (unless present), so no close pairs — fails. Trio \( A,B,C \): only \( AB \) is close → only 1 close pair → fails. - Veritas Home Health