Tutorial Activity 6

# Tutorial Activity 6 - MH 8300 Tutorial Activity 6 Mutilated...

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MH 8300 Tutorial Activity 6 Mutilated Chessboard Problem Group Members Name NTU Email ID Marks : /2

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MH 8300 Tutorial Activity 6 Mutilated Chessboard Problem Question 1. Consider the following mutilated chessboard with 5 white squares and 5 black squares. Figure 1: Mutilated Chessboard (a) Construct the chessboard graph based on the mutilated chessboard given. (b) Explain why the chessboard graph is bipartite. (c) Explain why the degree of any vertex is at most four.
(d) Given a matching M = {{ a 1 , b 3 }} after an initial iteration of the augmenting path approach, compute the maximum matching of the above chessboard graph. Apply the following steps of the augmenting path approach until a maximum matching is found. 2 nd iteration: (I) Using the matching M given, construct the auxiliary graph. (II) Write down a shortest path from s to t if it exist. (III) Is the matching maximum? If not, augment the matching using the path in (II) and write down the new matching M below.

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