3. Let P be the Petersen graph: (a) Find a maximum matching in P, and hence...
Let P stand for Petersen graph. Let P* stand for the graph by deleting a vertex from P. (a) Prove that the edge chromatic index of P is 4. Then, using the fact that the edge chromatic index of P is 4, deduce that P is non-Hamiltonian. (b) Prove that the edge chromatic index of P* is 4. Petersen graph
a graph theory homework questions parts c,d,e,f 6. Let G be the fllowing graph: 1) Fig, 7.7.1 (n) Does G have a perfect matching? (b) Find four maximum matchings in G. (c) Is there any maximum matching in G that contains the edge cl? (d) Find four maximal matchings (for definition, see Problem 7.6.20) that are not maximum. (e) Find in G (1) a maximum independent set, (ii) a minimum v-cover, and iii) n minimum c-cover. (f) Find the values...
2. Minimum and maximum spanning trees for the weighted Petersen graph. ei 4 (a) Find a minimum weighted spanning tree for the above weighted Petersen graph (b) Find a maximum weighted spanning tree for the above weighted Petersen graph
3. (a) Let Knbe the complete bipartite graph with n vertices in each part of its bipartition, where n 21. Determine the number of perfect matchings of Kn (b) A matching M in a graph Gis ca a mazimal matching if there exists no matching M' of G such that M is a proper subset of M' Prove that, for any graph G and any edges e,f of G which are not incident with a common vertex, there exists a...
Problem 2: Let G and H be the graphs below. For each graph, determine whether it is bipartite. If the graph is bipartite, determine whether it has a perfect matching. Justify your answer. Graph G: Graph H b
This is the Petersen graph: 4 6 8 2 3 (a) Give an argument to show that the Petersen graph does not contain a subdivision of K5. (b) Show that the Petersen graph contains a subdivision of K3,3.
Let X be a Poisson (mean = 5) and Let Y be a Poisson (mean = 4). Let Z = X + Y. Find P( X = 3 | Z = 6). Assume X and Y are independent. Show answers for P(A), P(B), P(AB), and and hence P(A|B). Here A = [X = 3], B = [Z = 6]
Please answer the question and write legibly (3) Prove that for a bipartite graph G on n vertices, we have a(G)- n/2 if and only if G has a perfect matching. (Recall that α(G) is the maximum size among the independent subsets of G.) (3) Prove that for a bipartite graph G on n vertices, we have a(G)- n/2 if and only if G has a perfect matching. (Recall that α(G) is the maximum size among the independent subsets of...
*Fourier Series a) Skatch the graph of f(x) from -2n <x <3x. Hence, determine whether the function is even, odd or neither (3 marks) b) Gihen that b find a, and a,. Hence, write f(x)in a Fourier series (11 marks)
Can Kruskal's algorithm be adapted to find (a) a maximum-weight tree in a weighted connected graph? (b) a minimum-weight maximal forest in a weighted graph? If so, how?