A Ramsey Theorem for Indecomposable Matchings
classification
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keywords
indecomposablematchinglongmatchingssegmentbrokencontaincontained
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A matching is indecomposable if it does not contain a nontrivial contiguous segment of vertices whose neighbors are entirely contained in the segment. We prove a Ramsey-like result for indecomposable matchings, showing that every sufficiently long indecomposable matching contains a long indecomposable matching of one of three types: interleavings, broken nestings, and proper pin sequences.
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