Transducing Linear Decompositions of Tournaments

Published 6 Jan 2026 in math.CO, cs.DM, and cs.LO | (2601.02999v1)

Abstract: Bojańczyk, Pilipczuk, and Grohe [LICS '18] proved that for graphs of bounded linear clique-width, clique-decompositions of bounded width can be produced by a CMSO transduction. We show that in the case of tournaments, a first-order transduction suffices. This implies that the logics CMSO and existential MSO are equivalent over bounded linear clique-width tournaments.

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