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

Aistis Atminas; Robert Brignall; Nicholas Korpelainen; Vadim Lozin; Vincent Vatter

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

Combinatorics 2015-04-28 v2

Authors: Aistis Atminas , Robert Brignall , Nicholas Korpelainen , Vadim Lozin , Vincent Vatter

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.

Keywords

permutation graphs well-quasi-order path omission clique omission structural decomposition infinite antichains

Cite

@article{arxiv.1312.5907,
  title  = {Well-Quasi-Order for Permutation Graphs Omitting a Path and a Clique},
  author = {Aistis Atminas and Robert Brignall and Nicholas Korpelainen and Vadim Lozin and Vincent Vatter},
  journal= {arXiv preprint arXiv:1312.5907},
  year   = {2015}
}

Comments

21 pages, 9 figures, to appear in Elec. J. Comb

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

Abstract

Keywords

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