2 Sentences With "diametrally"

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Since every apex graph is linkless embeddable, this shows that there are graphs that are linkless embeddable but not YΔY-reducible and therefore that there are additional forbidden minors for the YΔY-reducible graphs. Robertson's apex graph is shown in the figure. It can be obtained by connecting an apex vertex to each of the degree-three vertices of a rhombic dodecahedron, or by merging two diametrally opposed vertices of a four-dimensional hypercube graph. Because the rhombic dodecahedron's graph is planar, Robertson's graph is an apex graph.
It is unknown whether he was born already in Silesia or in exile, but he was brought up in Altenburg in the Holy Roman Empire and spent his childhood in the court of Emperor Frederick Barbarossa. After the recovery of Silesia by his father and uncle Mieszko I Tanglefoot in 1163, he moved there with the rest of his family and was there when probably began his activity in politics. However, the second marriage of his father with the German lady Christina changed diametrally his situation. Jarosław's stepmother began to intrigue, and Bolesław the Tall increasingly began to favored his younger sons.