Problem 1 3 Pts Let G And I Be Graphs Such That Gh Show That G Problem 2 4 Pts Is The Petersen Graph Bipartite 1 (61.01 KiB) Viewed 722 times
Please provide a mathematical proof for PROBLEM 3 ONLY,
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Problem 1 (3 pts). Let G and I be graphs such that GH. Show that Ğ=. Problem 2 (4 pts). Is the Petersen graph bipartite? What is its independence number? Justify your answer Problem 3 (6 pts). Prove that each of the following graphs is isomorphic to the Petersen Graph: 女 Problem 4 (3 pts). Suppose Kn decomposes into edge-disjoint triangles. Prove that 6 | n-1 or 6 n-3. Problem 5 (4 pts). Show that in a graph G, every closed odd walk contains an odd cycle.
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