Well-Quasi-Order for Permutation Graphs Omitting a Path and a Clique

  • Aistis Atminas
  • Robert Brignall
  • Nicholas Korpelainen
  • Vadim Lozin
  • Vincent Vatter
Keywords: well-quasi-order, permutation graphs, permutations, graphs


We consider well-quasi-order for classes of permutation graphs which omit both a path and a clique. Our principle result is that the class of permutation graphs omitting $P_5$ and a clique of any size is well-quasi-ordered. This is proved by giving a structural decomposition of the corresponding permutations. We also exhibit three infinite antichains to show that the classes of permutation graphs omitting $\{P_6,K_6\}$, $\{P_7,K_5\}$, and $\{P_8,K_4\}$ are not well-quasi-ordered.
Article Number