Let G be a graph. Carry out the following steps: (1) If G is not connected3 or if G contains a vertex of odd degree, STOP: the problem has no solution. (2) (We now know that G is connected and that all vertices of G have even degree.) Choose an edge e1, consider each permutation […]

A frequent problem is to order all permutations of a given set in such a way that two subsequent permutations differ by only a transposition. Show that this problem leads to the question whether a certain graph is Hamiltonian. Draw the graph for the case n = 3. The problem of finding Euler tours has

We want to find out in which cases the closed trail C0 constructed in Example 2.1.2 (2) is already necessarily Eulerian. An Eulerian graph is called arbitrarily traceable from v0 if each maximal trail beginning in v0 is an Euler tour; here maximal means that all edges incident with the end vertex of the trail

We construct a digraph G whose vertices are the single parts, modules, and finished products occurring in an industrial process. We want the edges to signify how many single parts or intermediary modules are needed for assembling bigger modules or finished products. That is, we assign weight w(i, j) to edge ij if we need

Show that an r-regular non-bipartite graph does not necessarily admit a 1-factorization, even if it has an even number of vertices. Hint: Consider the Petersen graph. Let G be a graph on 3n vertices. A 2-factor of G is called a triangle factor or a -factor if it is the disjoint union of n cycles

Decompose the graph K9 into _-factors. Hint: There is no cyclic decomposition as in Figure 7.2. Decompose the graph K6n−2 into 3-factors. Hint: Use Theorem 7.2.9. Readers interested in seeing more results on 1-factorizations and graph decompositions in general should consult the monographs [Bos90] and [Wal97].

Is the US a declining power? Elaborate, discuss implications, and illustrate. The post Is the US a declining power? Elaborate, discuss implications, and illustrate. appeared first on Essay Lane.

Research Design: A. Explain the research design and methods you will use, justifying why they are appropriate for your research study. B. Describe the key variables from primary and/or secondary data sources that you will use to analyze your research problem. C. Explain the key dependent and independent variables. In other words, how would the

The Lesson Walk-through (20 mins max) 1. What are your lesson objectives? 2. End goals: In the box below please outline what the end goals are of the lesson. ie what would you expect the students to have learnt or understood by the end of the lesson? (Often called lesson outcomes). 3. The opening of

Description Based on the information provided in the final project case study Maruti Suzuki India: Defending Market Leadership in the A-Segment , identify the data provided in the case study that is qualitative in nature and can be used to help answer your research question. Select one or two tables of qualitative data and describe