(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

SOLVED: Consider a planar drawing of a graph all whose faces, includingthe outer one, are triangular (i.e., have 3 vertices). To eachvertex we arbitrarily assign one of the labels 1, 2, 3. Prove thatthere are an even number of faces whose vertices get all threelabels.

Show that in a simple planar graph G, there are at least four v... | Filo

Planar Graph Perfect Matching is in NC