Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 324 / 3 / b / i / Solution

The vertices $v_2,v_3,v_5$ form a triangle in a graph, so every cut of a graph leaves at least one of their three edges uncut. Hence the cut size is at most four. TakeThe crossing edges are $(1,5),(2,3),(3,5),(4,5)$, so $C=4$. The upper bound is attained and this is a maximum cut.