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Q1 In this question, use the graph in Figure 1 and the initial matching M = {(a, A), (b, B)}. A a B b с d D Figure 1: Extend this matching (a) Starting from M, find a larger matching (i.e. show M isn't maximal). (b) Starting from M again, transform the graph so that Ford-Fulkerson can be applied and the initial matching M is the initial flow. (c) There are two augmenting paths. Find both. (d) Use the augmenting path involving c to augment the flow. (e) Run Ford-Fulkerson one more time, to find a min-cut. (f) Use the min-cut to identify a vertex cover V of the same size as your maximum-sized matching i.e. |V| = |M'|.

Q1 In this question, use the graph in Figure 1 and the initial matching M = {(a, A), (b, B)}. A a B b с d D Figure 1: Extend this matching (a) Starting from M, find a larger matching (i.e. show M isn't maximal). (b) Starting from M again, transform the graph so that Ford-Fulkerson can be applied and the initial matching M is the initial flow. (c) There are two augmenting paths. Find both. (d) Use the augmenting path involving c to augment the flow. (e) Run Ford-Fulkerson one more time, to find a min-cut. (f) Use the min-cut to identify a vertex cover V of the same size as your maximum-sized matching i.e. |V| = |M'|.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q1 In this question, use the graph in Figure 1 and the initial matching M = {(a, A), (b, B)}. A a B b с d D Figure 1: Extend this matching (a) Starting from M, find a larger matching (i.e. show M isn't maximal). (b) Starting from M again, transform the graph so that Ford-Fulkerson can be applied and the initial matching M is the initial flow. (c) There are two augmenting paths. Find both. (d) Use the augmenting path involving c to augment the flow. (e) Run Ford-Fulkerson one more time, to find a min-cut. (f) Use the min-cut to identify a vertex cover V of the same size as your maximum-sized matching i.e. |V| = |M'|.
Transcribed Image Text:Q1 In this question, use the graph in Figure 1 and the initial matching M = {(a, A), (b, B)}. A a B b с d D Figure 1: Extend this matching (a) Starting from M, find a larger matching (i.e. show M isn't maximal). (b) Starting from M again, transform the graph so that Ford-Fulkerson can be applied and the initial matching M is the initial flow. (c) There are two augmenting paths. Find both. (d) Use the augmenting path involving c to augment the flow. (e) Run Ford-Fulkerson one more time, to find a min-cut. (f) Use the min-cut to identify a vertex cover V of the same size as your maximum-sized matching i.e. |V| = |M'|.
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