(a) [BB] Show that the graph is planar by drawing an isomorphic plane graph with straight edges. (b) [BB] Label the regions defined by your plane graph and list the edges which form the boundary of each region. (c) [BB] Verify that V-E R=2, N ≤2 E, and E ≤3 V-6 (where, as defined in the proof of Corollary 14.1 .3, N is the sum of the numbers of edges on the boundaries of all regions). | Numerade

consider a planar drawing of a graph all whose faces including the outer one are triangular ie have 3 vertices to each vertex we arbitrarily assign one of the labels 1 2 3 prove that there a 44323

Convince yourself by drawing several examples that every 4 -val... | Filo

9.7 Give an example of each of the following or explain why no such example exists.(a) a planar graph of order 4.(b) a nonplanar graph of order 4.(c) a nonplanar graph of order 6 that contains neither K5 nor K3,3 as a subgraph.(d) a plane graph having 5 vertices, 10 edges and 7 regions.(e) a planar graph of order n ≥ 3 and size m with m = 3n - 6.(f) a nonplanar graph of order n ≥ 3 and size m with m = 3n - 6.

Give an example of (i) a non-planar graph that is not homeomorphic to K5 or K3,3; (ii) a non-planar graph that is not contractible to K5 or K3,3. Why does the existence of these graphs not contradict Theorems 4.2 and 4.3 ? | Numerade

Planar Graph Perfect Matching is in NC