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Sat 5 Nov, 2005 03:17 pm
Let G be 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.
(iii). Try to prove the four-color theorem by adapting the above proof of the five-color theorem. At what point does the proof fail?
How do you answer part II?
I can't figure out how to do the second part of the problem. if you could e-mail me the solution i'd appreciate it
thanks,
gs
email:
[email protected]
Hi! Same here. I can't do parts (ii) and (iii). Please help!