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Consejo Nacional de Ciencia y Tecnología, CONACYT: 106432
Generically Dependent Continuant
RDF description of Book drawings of complete bipartite graphs - http://orbis.uaslp.mx/vivo/individual/scopus3972
Article
2-page crossing number; Book crossing number; Complete bipartite graphs; Zarankiewicz conjecture
Book drawings of complete bipartite graphs
We recall that a book with k pages 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 νk(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 Kk 1,n for k∈{3,4,5,6}. We also prove the general asymptotic estimate lim k→∞limn→∞νk(Kk 1,n)/(2n2/k2)=1. Finally, we give general upper bounds for νk(Km,n), and relate these bounds to the k-planar crossing numbers of Km,n and Kn. © 2013 Elsevier B.V. All rights reserved.
We recall that a book with k pages 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 νk(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 Kk%2b1,n for k∈{3,4,5,6}. We also prove the general asymptotic estimate lim k→∞limn→∞νk(Kk%2b 1,n)/(2n2/k2)=1. Finally, we give general upper bounds for νk(Km,n), and relate these bounds to the k-planar crossing numbers of Km,n and Kn. © 2013 Elsevier B.V. All rights reserved.
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