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Journal of the ACM
In 1979, Bernhart and Kainen conjectured that graphs of fixed genus g > 1 have unbounded pagenumber. In this paper. it is proven that genus g graphs can be embedded in 0(g) pages, thus disproving the conjecture. An 0( fi) lower bound is also derwed. The first algorithm in the literature for embedding an arbitra~graph in a book with a non-trlwal upper bound on the number of pages M presented. First, the algorithm computes the genus g of a graph using the algorithm of Filotti, Miller, Reif (doi:10.1145/146637.146643 fatcat:hlgzjpndfjfqxomekkalifuc3u