A Ramsey Theorem for Indecomposable Matchings
James Fairbanks
TL;DR
This paper proves a Ramsey-like theorem for indecomposable matchings, demonstrating that long indecomposable matchings necessarily contain large submatchings of specific structured types, such as interleavings, broken nestings, or proper pin sequences.
Contribution
It introduces a new Ramsey-type result for indecomposable matchings, identifying guaranteed large structured submatchings within sufficiently long indecomposable matchings.
Findings
Every sufficiently long indecomposable matching contains a large submatching of a specific type.
Identifies three key types of structured indecomposable matchings.
Establishes a Ramsey-like property for the class of indecomposable matchings.
Abstract
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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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory · Computability, Logic, AI Algorithms