Is the n-dimensional cube qn hamiltonian

Reference no: EM1324891

Q1. Suppose that G is a forest Consisting of k trees T1, T2, ..., Tk. Furthermore, suppose that Ti has order ni, for 1<=i<=k. What is the size of G? Prove your answer.

Q2. Is the n-dimensional cube Qn Hamiltonian? Prove your answer.

Q3. Suppose that G is trianglt free and does not contain P4 as an induced subgraph(that is, if G contains P4, then G contains an edge between vertices of P4 not in P4.) is G Bipartite? Prove your answer, Hint: Start by assuming an odd cycle of minimum length.

Reference no: EM1324891

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