Algebraic Methods for Reducibility in Nowhere-Zero Flows
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Date
2007-09-25T20:53:28Z
Authors
Li, Zhentao
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
We study reducibility for nowhere-zero flows. A reducibility proof typically consists of showing that some induced subgraphs cannot appear in a minimum counter-example to some conjecture. We derive algebraic proofs of reducibility.
We define variables which in some sense count the number of nowhere-zero flows of certain type in a graph and then deduce equalities and inequalities that must hold for all graphs. We then show how to use these algebraic expressions to prove reducibility. In our case, these inequalities and equalities are linear. We can thus use the well developed theory of linear programming to obtain certificates of these proof.
We make publicly available computer programs we wrote to generate the algebraic expressions and obtain the certificates.
Description
Keywords
graph theory, nowhere-zero flow, reducibility, algebraic method, equalities, inequalities