Abstract
We study unit interval graphs and bipartite permutation graphs partially ordered by the induced subgraph relation. It is known that neither of these classes is well-quasi-ordered, since each of them contains an infinite antichain. We show that in both cases the antichains are canonical in the sense that any subclass of unit interval or bipartite permutation graphs containing only finitely many graphs from the respective antichain is well-quasi-ordered.
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Research supported by the Centre for Discrete Mathematics and Its Applications (DIMAP), University of Warwick.
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Lozin, V.V., Mayhill, C. Canonical Antichains of Unit Interval and Bipartite Permutation Graphs . Order 28, 513–522 (2011). https://doi.org/10.1007/s11083-010-9188-7
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DOI: https://doi.org/10.1007/s11083-010-9188-7