Transducing Linear Decompositions of Tournaments
Combinatorics
2026-01-07 v1 Discrete Mathematics
Logic in Computer Science
Abstract
Boja\'nczyk, 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.
Cite
@article{arxiv.2601.02999,
title = {Transducing Linear Decompositions of Tournaments},
author = {Colin Geniet and Fatemeh Ghasemi and Mamadou Moustapha Kanté},
journal= {arXiv preprint arXiv:2601.02999},
year = {2026}
}
Comments
30 pages, 4 figures