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question let g be a connected graph and let c be any circuit in g that does not contain every vertex of c let g be the
question a prove that if a walk in a graph contains a repeated edge then the walk contains a repeated vertexb explain
question a traveler in europe wants to visit each of the cities shown on the map exactly once starting and ending in
question for what values of m and n does the complete bipartite graph on m n vertices havea an euler circuitb a
question determine which of the graphs have euler circuits if the graph does not have an euler circuit explain why not
question the solution for example shows a graph for which every vertex has even degree but which does not have an euler
question each of a-c describes a graph in each case answer yes no or not necessarily to this question does the graph
question in find hamiltonian circuits for those graphs that have them explain why the other graphs do
question determine whether there is a primary key for the relation in exampleexample let r be the relation on z times z
question discuss the use of the critical path method cpm to find the shortest time for the completion of a project how
question discuss the use of the program evaluation and review technique pert to schedule the tasks of a large
question describe how equivalence classes can be used to define the rational numbers as classes of pairs of integers
question given the matrix representing a relation on a finite set find the matrix representing the transitive closure
question find the transitive closure of a relation of your choice on a set with at least 20 elements either use a
question compute the number of different equivalence relations on a set with n elements for all positive integers n not
question look up the original papers by warshall and by roy in french in which they develop algorithms for finding
question the minimum vertex cover problem min-vcp is a minimization problem where one searches for a vertex cover of
question one observes that the protocol umc is based on a nondeterministic protocol that simply guesses the position j
question let a be a randomized algorithm computing a function f with probax fx ge 13 for every argument x of f assume
question consider the probabilistic experiment given by the protocol r2 define two indicator variables x1 and x2 where
question consider the following problem given a set a of elements with a linear order and a positive integer k k le a
question modify the randomized quicksort by stopping all computations longer than 16 middot n middot log2 n with the
question let r be a quasi-ordering and let s be the relation on the set of equivalence classes of r cap r-1 such that c
question let r be the relation on the set of all functions from z to z such that f g belongs to r if and only if f is