Given the graph determine if the following reasoning is correct to show that the graph does not have a Hamiltonian cycle. 1. LaTeX: 1V1=6, |E|=8. [Select] 2. Thus, to obtain a Hamiltonian cycle we would need to remove exactly 2 edges. [Select] 3. After the removal of such edges, each vertex should have degree 2 [Select] 4. Vertices 1, 3, 5, and 6 have degree 3. (Select] 5. We then need to remove 4 edges (one for each of the vertices 1, 3, 4, and 6). [Select] 6. This contradicts 2., so the graph does not have a Hamiltonian cycle. Given the graph determine if the following reasoning is correct to show that the graph does not have a Hamiltonian cycle. 1. LaTeX: 1V1=6, |E|=8. [Select] 2. Thus, to obtain a Hamiltonian cycle we would need to remove exactly 2 edges. [Select] 3. After the removal of such edges, each vertex should have degree 2 [Select] 4. Vertices 1, 3, 5, and 6 have degree 3. (Select] 5. We then need to remove 4 edges (one for each of the vertices 1, 3, 4, and 6). [Select] 6. This contradicts 2., so the graph does not have a Hamiltonian cycle