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Flows in graphs present an important topic in modern mathematics with many applications in practice and a significant impact on many problems from discrete mathematics. Nowherezero flow in graphs present a dual concept for graph coloring problems. We apply methods of linear algebra for nowherezero flow problems. We present several results regarding the 5flow conjecture. In particular, we give restrictions regarding cyclical edge connectivity and girth for a smallest counterexample to the conjecture. We present also application for edgecoloring of planar cubic graphs. Furthermore we present a decomposition formula for flow polynomials on graphs. The book is devoted for graduate students and researchers dealing with combinatorics.
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