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Let G=(V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected.
a) Show that the vector x which is indexed by the edges E and for which xe = 1/5 for all e in E is in the Perfect Matching Polytope PPM.
b) Use your result in a) to show that G must have a perfect matching.
c) Show that b) may not be true if G is only 1-edge connected (but still has degree 5 everywhere) by giving an example of such a graph G which has no perfect matching.
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for i=1 to n if a[i}>7 for j=2 to n a[j]=a{j}+j for n=2 to n a[k]=a[j]+i else if a[1]>4 && a[1] for 2 to a[1] a[j]= a{j]+5 else for 2to n a[j]=a[j]+i ..
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