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Matrix Choosability

✍ Scribed by Matt DeVos

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 149 KB
Volume: 90
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3026

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✦ Synopsis

Let F be a finite field with p c elements, let A be a n_n matrix over F, and let k be a positive integer. When is it true that for all X 1 , ...,

Ax= y? It is trivial that A has this property for k= p c &1 if det(A){0. The permanent lemma of Noga Alon proves that if perm(A){0, then A has this property for k=1. We will present a theorem which generalizes both of these facts, and then we will apply our theorem to prove ``choosability'' generalizations of Jaeger's 4-flow and 8-flow theorems in Z k p .

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