On the Crossing Number of Almost Planar Graphs‪.‬

If G is a plane graph and x, y [member of] V (G), then the dual distance of x and y is equal to the minimum number of crossings of G with a closed curve in the plane joining x and y. Riskin [7] proved that if [G.sub.0] is a 3-connected cubic planar graph, and x, y are its vertices at dual distance d, then the crossing number of the graph [G.sub.0]) + xy is equal to d. Riskin asked if his result holds for arbitrary 3-connected planar graphs. In this paper it is proved that this is not the case (not even for every 5-connected planar graph [G.sub.0]). Povzetek: Analizirana je Riskinova teza o planarnih grafih.