3. For each of the following graphs, determine if the graph is planar. If it is,...
For each of the following graphs draw a planar representation or show that it has a subgraph homeomorphic to K5 or K3,3: For each of the following graphs draw a planar representation or show that it has a subgraph homeomorphic to K; or K3,3: (a) (b) (c) (d)
8. Determine whether each graph is planar. If the graph is planar, redraw it so that no edges cross; otherwise, find a subgraph homeomorphic to either K5 or K3,3 (a) (10 pts) See Figure in 3. (b) (5 pts) See Figure in 4 Figure 3: Graph for Question 8(a) مل a e С Figure 4: Graph for Question 8(b)
Determine if each of the following graphs is planar. Graph G1: [ Select ] ["Non-planar", "Planar"] Graph G2: [ Select ] ["Planar", "Non-planar"] Graph G3: [ Select ] ["Non-planar", "Planar"] ...
Please do NOT apply Kuratowski's theorem. Because of the symmetry between edges in each graph, it suffices to find a plane embedding for each graph removing an edge (draw an example). Problem 4. (5 points each.) 1. Show that when any edge is removed from K3,3, the resulting subgraph is planar. 2. Show that when any edge is removed from K5, the resulting subgraph is planar.
3. Which of the following graphs are planar? Find K 3.3 or Ks configurations in the nonplanar graphs (almost all are K3,3). (k) (1)
Are the following graphs planar? If so, show a planar representation and if not, explain why not. ь. Are the following graphs planar? If so, show a planar representation and if not, explain why not. ь.
(a) Sketch accurate graphs of K5 and K2,3. Label each graph as either planar or non-planar.
Jul It Uul D Question 35 2 pts Let G be a graph. What is the contrapositive of the statement "If G is planar, then G has a 4-coloring"? Gis planar and G does not have a 4-coloring. Gis not planar or G has a 4-coloring. If G has a 4-coloring, then G is planar. If G does not have a 4-coloring, then G is not planar. If G is not planar, then G does not have a 4-coloring. If...
8. The thickness θ(G) of a graph is the minimum number of planar graphs whose union is G (Hence θ(G)-1 if and only if G is planar.) For a simple (p, q)-graph G, show that θ(G) 3 1 8. The thickness θ(G) of a graph is the minimum number of planar graphs whose union is G (Hence θ(G)-1 if and only if G is planar.) For a simple (p, q)-graph G, show that θ(G) 3 1
3. Vertex Cover on Planar Graphs. The problem Planar Vertex Cover is to find a smallest set C of vertices in a given planar graph G such that every edge in G has at least one endpoint in C. It is known that Planar Vertex Cover is NP-hard. Develop a polynomial time approximation scheme (PTAS) for the problem.