(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.

Planar Graph Perfect Matching is in NC - Microsoft Research