Well-Quasi-Order for Permutation Graphs Omitting a Path and a Clique
Abstract
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 P5 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 \P6,K6\, \P7,K5\, and \P8,K4\ are not well-quasi-ordered.
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