A note on finding large transversals efficiently

In an nxn array filled with symbols, a transversal is a collection of entries with distinct rows, columns and symbols. In this note we show that if no symbol appears more than ßn times, the array contains a transversal of size (1-ß/4 - o(1))n. In particular, if the array is filled with n symbols, ea...

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Detalles Bibliográficos
Autores: Anastos, Michael, Morris, Patrick Wyndham|||0000-0001-9359-0748
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/431885
Acceso en línea:https://hdl.handle.net/2117/431885
https://dx.doi.org/10.1002/jcd.21990
Access Level:acceso abierto
Palabra clave:Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Descripción
Sumario:In an nxn array filled with symbols, a transversal is a collection of entries with distinct rows, columns and symbols. In this note we show that if no symbol appears more than ßn times, the array contains a transversal of size (1-ß/4 - o(1))n. In particular, if the array is filled with n symbols, each appearing n times (an equi-n square), we get transversals of size (3/4 - o(1))n. Moreover, our proof gives a deterministic algorithm with polynomial running time, that finds these transversals.