Martin Kochol

Flows in Graphs and Related Problems: Nowhere-zero Flows, Cycle Covers, and Combinatorial Optimization Martin Kochol

Flows in graphs present a basis for solving many problems in modern mathematics, having applications in practice and significant theoretical impact in various areas on discrete mathematics, such as graph coloring, labeling, covering of graphs, matroid theory, combinatorial optimization, and statistical physics. In the book are considered several theoretical aspects of flows in graphs. The results are divided into three parts. In the first part, nowhere-zero group- and integer-valued flows are studied, together with related areas regarding snarks and graph colorings. The second part contains results about cycle double coverings of graphs, hamiltonian cycles and dominating cycles. The last part is devoted to flows in combinatorial optimization and some related areas from transversal theory and latin squares. The work was presented as DSc. Thesis in the Academy of Sciences of Czech Republic. It can be useful for advanced students and researchers interested in combinatorics and graph theory.