Euler's Formula for Connected Planar Graphs - Search Videos

(i) Use Euler's formula to prove that, if G is a connected planar graph of girth 5 with n vertices and m edges, then m ≤5 / 3(n-2). Deduce that the Petersen graph is non-planar. (ii) Obtain an inequality, generalizing that in part (i), for connected planar graphs of girth r. | Numerade

(i) Use Euler's formula to prove that, if G is a connected planar graph of girth 5 with n vertices and m edges, then m ≤5 / 3(n-2). Deduce that the Petersen graph is non-planar. (ii)

(i) Use Euler's formula to prove that, if G is a connected planar graph of girth 5 with n vertices and m edges, then m ≤5 / 3(n-2). Deduce that the Petersen graph is non-planar. (ii) Obtain an inequality, generalizing that in part (i), for connected planar graphs of girth r.

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