Matroids (Q5960194)

This review is devoted to the description of the main results of the theory of matroids. Translated from Russian and likely to have been written in the mid 1990s, the review begins with equivalent axiomatizations of matroids (including a table relating these axiomatizations), examples of matroids, and matroid constructions. The range of topics is extensive and includes matroid representations, Tutte polynomials, the critical problem, and matroid oracles. The survey ends with a section that highlights the importance of matroids to combinatorial optimization as well as describing applications in rigidity and electrical networks. Open problems are included throughout. Readers should be aware that, possibly due to translation, some of the notation is not standard. For example, `homogeneous' is used for `uniform' and `narrowing' is used for `restriction'. The survey is well written, descriptive, and informative.