Problem B: Show that the following graph is non planar by showing the K3,3 configuration it...
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)
3. For each of the following graphs, determine if the graph is planar. If it is, draw a plane representation of the graph; if not, indicate a subgraph homeomorphic to Kor K3,3 G
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)
Re-draw the graph below showing that it is planar.
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"] ...
(a) Sketch accurate graphs of K5 and K2,3. Label each graph as either planar or non-planar.
This is the Petersen graph: 4 6 8 2 3 (a) Give an argument to show that the Petersen graph does not contain a subdivision of K5. (b) Show that the Petersen graph contains a subdivision of K3,3.
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.
Show that the following graph is planar by redrawing it so that no edges cross each other.
5. Let G is a simple planar graph containing no triangles. (i) Using Euler's formula, show that G contains a vertex of degree at most 3. (ii) Use induction to deduce that G is 4-colorable-(v). 5. Let G is a simple planar graph containing no triangles. (i) Using Euler's formula, show that G contains a vertex of degree at most 3. (ii) Use induction to deduce that G is 4-colorable-(v).