DOI: 10.24193/fpt-ro.2025.1.13

Authors: Shravan Luckraz

Abstract: We represent the problem of the existence of a stable matching as a fixed point problem and show that a generalization of the no-odd ring condition is necessary and sufficient for the existence of a stable matching. Our result uses a generalization of the Abian's fixed point theorem.

Key Words and Phrases: Existence of stable matchings, roommate problem, fixed point theorem, graph theory, existence of equilibrium.

2010 Mathematics Subject Classification: 37C25, 91B68, 06B23.

Published on-line: February 1st, 2025.

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