Question: I need help in these 6 questions. Extensive explanation would be appreciated. Problem 1 (10 points) Is there a convex polyhedron consisting of four triangles,

I need help in these 6 questions. Extensive explanation would be appreciated.

Problem 1 (10 points) Is there a convex polyhedron consisting of four triangles, six pentagons, and four octagons (ES-sided polygon)? Problem 2 (10 points) What is the Smallest number of colors you need to properly color the vertices of K45? That is, nd the chromatic number of the graph. (Please sketch the graph and show why you have the answer.) Problem 3 (10 points) For which t and a does the graph Km,\" contains an Euler path? An Euler circuit? Explain in detail. Problem 4 (10 points) For which a does the graph Kn contains a Hamilton path? A Hamilton circuit? Explain in detail. Problem 5 (10 points) Find the sequence generated by the generation function. (Show each steps how to nd the sequences.) :1: 1+2: Problem 6 (10 points) Find the sequence generated by the generation function. (Show each steps how to nd the sequences.) 33' (l + as)2

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