Improved Lower Bounds for the 2-Page Crossing Numbers of Km, n and Kn via Semidefinite Programming
نویسندگان
چکیده
It has been long conjectured that the crossing numbers of the complete bipartite graph Km,n and of the complete graph Kn equal Z(m,n) := ⌊
منابع مشابه
Improved Lower Bounds on Book Crossing Numbers of Complete Graphs
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 k-page crossing number νk(G) of a graph G is the minimu...
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It has long been conjectured that the crossing number cr(Km,n) of the complete bipartite graph Km,n is equal to Z(m,n) := bm−1 2 cb2 cbn−1 2 cb2 c. Another long-standing conjecture is that the crossing number cr(Kn) of the complete graph Kn is equal to Z(n) := 4b2 cbn−1 2 cbn−2 2 cbn−3 2 c. In this talk, I will outline a new method that improves the asymptotic lower bounds to 0.83Z(m, n) and 0....
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عنوان ژورنال:
- SIAM Journal on Optimization
دوره 22 شماره
صفحات -
تاریخ انتشار 2012