It has been longâ€“conjectured that the crossing number cr(Km,n) of the complete bipartite graph Km,n equals the Zarankiewicz Number Z(m, n) := âŒŠ mâˆ’1 2 âŒ‹âŒŠ 2 âŒ‹âŒŠ 2 âŒ‹âŒŠ 2 âŒ‹. Another longâ€“standingâ€¦ (More)

Let a be an integer. It is proved that for any s and k, there exists a constant N = N(s, k, a) such that every 31 2 (a+1)-connected graph with at least N vertices either contains a subdivision ofâ€¦ (More)

It is shown that for any positive integers k and w there exists a constant N = N(k, w) such that every 7-connected graph of tree-width less than w and of order at least N contains K3,k as a minor.â€¦ (More)

There are several graphs H for which the precise structure of graphs that do not contain a minor isomorphic to H is known. In particular, such structure theorems are known for K5 [13], V8 [8] andâ€¦ (More)

A review of 300 cases of breast cancer in a community hospital was undertaken to document who made the initial discovery of the breast lesion. In this series, the woman discovered her own cancer inâ€¦ (More)

The Petersen family consists of the seven graphs that can be obtained from the Petersen Graph by Y2and 2Y-exchanges. A splitter for a family of graphs is a maximal 3-connected graph in the family. Inâ€¦ (More)