Local Out-Tournaments with Upset Tournament Strong Components I: Full and Equal {0,1}-Matrix Ranks

Authors

Kim A. S. Factor, Marquette UniversityFollow
Rebecca M. Kohler, Marquette University
Jason M. Derby, GE Healthcare

Document Type

Article

Language

eng

Format of Original

15 p.

Publication Date

2010

Publisher

Charle Babbage Research Center

Source Publication

Ars Combinatoria

Source ISSN

0381-7032

Abstract

A digraph D is a local out-tournament if the outset of every vertex is a tournament. Here, we use local out-tournaments, whose strong components are upset tournaments, to explore the corresponding ranks of the adjacency matrices. Of specific interest is the out-tournament whose adjacency matrix has boolean, nonnegative integer, term, and real rank all equal to the number of vertices, n. Corresponding results for biclique covers and partitions of the digraph are provided.

Comments

Published version. Ars Combinatoria, Volume 95, No. 1 (2010). © 2010 Charles Babbage Research Center. Used with permission.

Recommended Citation

Factor, Kim A. S.; Kohler, Rebecca M.; and Derby, Jason M., "Local Out-Tournaments with Upset Tournament Strong Components I: Full and Equal {0,1}-Matrix Ranks" (2010). Mathematics, Statistics and Computer Science Faculty Research and Publications. 13.
https://epublications.marquette.edu/mscs_fac/13