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

SOLVED:Draw a planar representation of each graph.

If G is a planar graph with a vertices, ecdges, f taces and k ... | Filo

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

Show that every planar graph G can be colored using six or fewer colors. [Hint: Use mathematical induction on the number of vertices of the graph. Apply Corollary 2 of Section 10.7 to find a vertex v with deg(v) ≤5 . Con- sider the subgraph of G obtained by deleting v and all edges incident with it.] | Numerade

Determine whether the given graph is planar. If so, draw it so that no edges cross. | Numerade