1)Find the number of factor trees of the graph below
2)Given the graph G of the figure below. What is the number of factor trees of G that contain the path 2-3-4-5-6-7-11 ?
3)Suppose we want to schedule the courses of the exam period so that there is no student who has two courses on the same day. The data is as follows: we have the courses numbered with numbers 1,2,...,7 and the diagram below which shows if there is a student enrolled in two courses at the same time. More specifically, if there is an asterisk in position i,j, this means that there is a student enrolled in course i and course j at the same time. What is the minimum number of days we need to schedule the exams?
4)Let T be a tree with 20 vertices, for which we know that each vertex has degree either 1 or 4. We want to add to this tree the minimum number of edges possible (without adding extra vertices) so that the resulting graph has an Euler cycle . How many edges should we add?
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