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arXiv · 1312.5907

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

Aistis Atminas·Robert Brignall·Nicholas Korpelainen·Vadim Lozin·Vincent Vatter
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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 $P_5$ 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.

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Aistis Atminas, Robert Brignall, Nicholas Korpelainen, Vadim Lozin, Vincent Vatter. 2015-04-27. Well-Quasi-Order for Permutation Graphs Omitting a Path and a Clique. https://arxiv.org/abs/1312.5907

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