{ "q01": { "type": "blank", "question": "\n\n\nA ____ is an ordering of nodes in a ____ graph such that if there is a path\nfrom a node a to node b, then node a appears ____ b in the ordering. An\n____ graph always has at least one such ordering. According to Wikipedia,\nwe can use ____'s algorithm compute this ordering of nodes in a graph.\n\n\n" }, "q02": { "type": "multiple", "question": "\n\n\nGiven the following graph, which of the following orders are topological\nsorts (select all that apply)?\n\n
\n\n
\n\n
\n", "responses": { "one": "A, B, C, D, E, F, G, H", "two": "C, A, B, E, D, F, G, H", "three": "A, B, C, E, D, H, G, F", "four": "B, A, D, C, H, E, G, F", "five": "A, B, D, F, C, E, G, H", "six": "C, B, E, A, D, H, F, G", "seven": "A, D, H, F, G, E, B, C", "eight": "B, A, D, F, C, G, H, E" } }, "q03": { "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" }, "q04": { "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." } }, "q05": { "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." } }, "q06": { "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." } }, "q07": { "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" }, "q08": { "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" } }