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Paths, trees and cycles in tournaments. (English) Zbl 0894.05032
Two authors who have done much recent work in digraphs prepared this survey of core topics in tournaments. Most of the topics concern paths and cycles—Hamiltonian paths and cycles, paths with prescribed endvertices, cycles through or avoiding specified arcs, oriented paths and cycles, monochromatic paths in colored tournaments, and the count of certain paths and cycles. The problems of pancyclicity and path-connectivity are discussed. The other topics are trees, claws and modified paths. In each area, the authors give us the status of the major problems. They state important theorems and, in several instances, new problems arising from these results.

05C38 Paths and cycles
05C20 Directed graphs (digraphs), tournaments
05C05 Trees