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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/431885 |
| Online Access: | https://hdl.handle.net/2117/431885 https://dx.doi.org/10.1002/jcd.21990 |
| Access Level: | Open access |
| Keyword: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Summary: | 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. |
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