Embedding graphs in books: a layout problem with applications to VLSI design
SIAM Journal on Algebraic and Discrete Methods
Embedding planar graphs in four pages
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Cyclic-order graphs and Zarankiewicz's crossing-number conjecture
Journal of Graph Theory
The book crossing number of a graph
Journal of Graph Theory
On the pagenumber of complete bipartite graphs
Journal of Combinatorial Theory Series B
Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization
SIAM Journal on Optimization
Reduction of symmetric semidefinite programs using the regular $$\ast$$-representation
Mathematical Programming: Series A and B
Discrete Applied Mathematics
Random Structures & Algorithms
Solving Hard Mixed-Integer Programming Problems with Xpress-MP: A MIPLIB 2003 Case Study
INFORMS Journal on Computing
Fixed linear crossing minimization by reduction to the maximum cut problem
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
On the Shannon capacity of a graph
IEEE Transactions on Information Theory
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We recall that a book withkpages consists of a straight line (the spine) and k half-planes (the pages), such that the boundary of each page is the spine. If a graph is drawn on a book with k pages in such a way that the vertices lie on the spine, and each edge is contained in a page, the result is a k-page book drawing (or simply a k-page drawing). The page number of a graph G is the minimum k such that G admits a k-page embedding (that is, a k-page drawing with no edge crossings). The k-page crossing number@n"k(G) of G is the minimum number of crossings in a k-page drawing of G. We investigate the page numbers andk-page crossing numbers of complete bipartite graphs. We find the exact page numbers of several complete bipartite graphs, and use these page numbers to find the exactk-page crossing number of K"k"+"1","n for k@?{3,4,5,6}. We also prove the general asymptotic estimate lim"k"-"~lim"n"-"~@n"k(K"k"+"1","n)/(2n^2/k^2)=1. Finally, we give general upper bounds for @n"k(K"m","n), and relate these bounds to the k-planar crossing numbers of K"m","n and K"n.