For the following questions, assume all graphs are simple graphs.
Give a condition that is necessary but not sufficient for an undirected graph to have an Eulerian Path. Justify your answer.
Give two necessary conditions for an undirected graph to have a Hamiltonian Cycle. Justify your answer.
Draw a Complete Graph, K_(n), with n>6 that has a Hamiltonian Cycle but does not have an Eulerian Cycle. List the degrees of the vertices, draw the Hamiltonian Cycle on the graph and provide justification that there is no Eulerian Cycle.
For the following questions, assume all graphs are simple graphs.
1. Give a condition that is necessary but not sufficient for an undirected graph to have an Eulerian Path. Justify your answer.
2. Give two necessary conditions for an undirected graph to have a Hamiltonian Cycle. Justify your answer.
3. Draw a Complete Graph, Kn,with n > 6 that has a Hamiltonian Cycle but does not have an Eulerian Cycle. List the degrees of the vertices, draw the Hamiltonian Cycle on the graph and provide justification that there is no Eulerian Cycle