In graph theory the crossing number crg of a graph g is the lowest number of edge crossings of a plane drawing of the graph g for instance a graph is planar if and only if its crossing number is zero. 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 crossing numbers of graphs is an interesting topic in discrete geometry graph theory graph drawing and computer science though simple at its core it lends itself to ideas that are much more complex. The crossing number graphs were found by co author geoffrey exoo using his program gnubar nu represents a crossing number a bar suggests rectilinearity the many cubic graphs he tested were obtained from brendan mckays nauty program 13 . The problem of finding the crossing number of the complete graph has a more fuzzy history than its bipartite counterpart it is such a natural question that several people might have attacked it before giving up discouraged by its difficulty
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