Another template:
three-toothed comb inequalities

Every tour x satisfies the inequality

x(H,V-H) +x(T1,V-T1) +x(T2,V-T2) +x(T3,V-T3) 10

Separation algorithms for this template:

• heuristic, practical:
  • Padberg and Rinaldi (1987)
  • Grötschel and Holland (1991)
  • Clochard and Naddef (1993)
  • Applegate, Bixby, Chvátal, and Cook (1995)
  • Naddef and Thienel (1999)
• exact, polynomial-time, impractical:
  • Carr (1995)