Vladimir P. Korzhik

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A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by no more than one other edge. A non-1-planar graph G is minimal if the graph G − e is 1-planar for every edge e of G. We construct two infinite families of minimal non-1-planar graphs and show that for every integer n ≥ 63, there are at least 2(n−54)/4 nonisomorphic minimal(More)
It was proved earlier that there are constants M, c > 0 such that for every n M (resp., every n M , n / ≡ 0, 3mod 12) there are at least c2n/6 nonisomorphic nonorientable (resp., orientable) genus embeddings ofKn. In the present paper we show that for s 6 there are at least 2s−6 nonisomorphic OT-embeddings of K12s . As a byproduct, we give a relatively(More)