Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part of the text deals with traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, and the independent odd crossing number.It also includes applications of the crossing number outside topological graph theory. Aimed at graduate students and professionals in both mathematics and computer science The first book of its kind devoted to the topic Authored by a noted authority in crossing numbers

Reports on federal efforts to improve safety at the nation's railroad crossings. Analyzes progress made in reducing accidents and fatalities at crossings. Discusses federal and state strategies -- for distributing funds, developing technologies, and educating the public. Assesses the Dept. of Transportation's (DoT) progress in implementing its action plan for improving railroad crossing safety. Charts, tables and graphs.