{ "q01": { "type": "blank", "question": "\n\n\nA path that goes through each edge exactly once is called an ____ path,\nwhile a path that visits each node exactly once is a ____ path. A variant\nof either type of path that starts and ends at the same node is called a\n____.\n\nWhile there are efficient methods of determining if the former exists in a\ngraph, the existence of the latter is considered a ____ problem, where no\nefficient algorithm is known for solving the problem.\n\n\n" }, "q02": { "type": "multiple", "question": "\n\n\nFor an Eulerian path to exist in a graph, which of the following conditions\nare sufficient (choose all that apply)?\n\n\n", "responses": { "even": "The degree of each node is even.", "odd_even": "The degree of exactly two nodes is odd, and the degree of all other nodes is even.", "odd": "The degree of each node is odd.", "even_odd": "The degree of exactly two nodes is even, and the degree of all other nodes is odd." } }, "q03": { "type": "multiple", "question": "\n\n\nFor a Hamiltonian path to exist in a graph, which of the following\nconditions are sufficient (choose all that apply)?\n\n\n", "responses": { "complete": "The graph is complete.", "connected": "The graph is connected.", "degree": "The degree of each node is at least n/2.", "sum": "The sum of the degrees of each non-adjacent pair of nodes is at least n.", "even": "The degree of each node is even." } }, "q04": { "type": "multiple", "question": "\n

\nGiven the following graph, which of the following statements is true (choose all that apply)?\n

\n\n
\n \n
\n
\n", "responses": { "epath": "There is an Eulerian path.", "ecircuit": "There is an Eulerian circuit.", "hpath": "There is an Hamiltonian path.", "hcircuit": "There is an Hamiltonian circuit." } }, "q05": { "type": "blank", "question": "\n\nIn a ____ problem, we are interested in determining how much flow is\npossible to send from the ____ to the ____, while in a ____ problem, we\nwant to know the ____ set of edges that separates the two nodes of the\ngraph.\n\n\n" }, "q06": { "type": "blank", "question": "\n

\nGiven the following graph:\n

\n\n
\n \n
\n\n
\n
1. What is the maximum flow from 1 to 5? ____
2. \n
3. What is the minimum cut from 1 to 5? ____
4. \n
5. How many edges are in the minimum cut? ____
6. \n
\n
\n" } }