On the Pagenumber of Complete Bipartite Graphs

The pagenumberp(G) of a graphGis defined as the smallestnsuch thatGcan be embedded in a book withnpages. We give an upper bound for the page-number of the complete bipartite graphKm, n. Among other things, we provep(Kn, n)⩽⌊2n/3⌋+1 andp(K⌊n2/4⌋, n)⩽n−1. We also give an asymptotic result: min{m: p(Km, n)=n}=n2/4+O(n7/4).