Graph Theory: 57. Planar Graphs
5:54
YouTubeSarada Herke
Graph Theory: 57. Planar Graphs
A planar graph is a graph that can be drawn in the plane without any edge crossings. Such a drawing (with no edge crossings) is called a plane graph. A given plane graph divides the plane into regions and each region has a boundary that outlines it. We look at some examples and also give an informal proof of the fact that the complete bipartite ...
已浏览 24.8万 次2015年3月29日
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Show that any minor of a planar graph is planar. Deduce that a graph is planar if and only if it is the minor of a grid. (Grids are defined in Chapter 12.3.) | Numerade
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A planar graph G is said to be completely regular if the degrees of all vertices of G are equal and every region is bounded by the same number of edges. The graphs in Figs. 2-20(a) and 2-21(b) are completely regular, for example. Show that there are only five possible simple completely regular planar graphs, excluding the trivial graphs with degree ≤2. Sketch them. | Numerade
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