graph                        truth   broken   repaired
  single edge 0-1             none   cycle    none
  path 0-1-2-3                none   cycle    none
  triangle 0-1-2-0            cycle  cycle    cycle
  star, center 0              none   cycle    none
  two parallel edges 0=1      cycle  cycle    cycle
  forest: 0-1 and 2-3         none   cycle    none
  tree plus one chord         cycle  cycle    cycle
broken version wrong on   4 of 7 graphs
repaired version wrong on 0 of 7 graphs
