Ondrej Sýkora

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The bipartite crossing number problem is studied, and a connection between this problem and the linear arrangement problem is established. It is shown that when the arboricity is close to the minimum degree and the graph is not too sparse, then the optimal number of crossings has the same order of magnitude as the optimal arrangement value times the(More)
The antibandwidth problem consists of placing the vertices of a graph on a line in consecutive integer points in such a way that the minimum difference of adjacent vertices is maximized. The problem was originally introduced in [15] in connection with multiprocessor scheduling problems and can be also understood as a dual problem to the well known bandwidth(More)
We give drawings of a complete graphK n withO(n 4 log2 g/g) many crossings on an orientable or nonorientable surface of genusg ≥ 2. We use these drawings ofK n and give a polynomial-time algorithm for drawing any graph withn vertices andm edges withO(m 2 log2 g/g) many crossings on an orientable or nonorientable surface of genusg ≥ 2. Moreover, we derive(More)
In the circular (other alternate concepts are outerplanar, convex and one-page) drawing one places vertices of a n−vertex m−edge connected graph G along a circle, and the edges are drawn as straight lines. The smallest possible number of crossings in such a drawing of the graph G is called circular (outerplanar,convex, or one-page) crossing number of the(More)
Accuracy of fit of denture bases is critical to adequate retention. This study compared the dimensional change of a newer continuous-injection technique with a standard trial-pack technique as determined by measuring the posterior palatal border opening. The influence of palate shape and immersion were also assessed. Stone casts were made from master moulds(More)