Q 1 In this question, use the graph in Figure 1 and the initial matching M = {(a, A), (b, B)}. A d B 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'|.

Q 1 In this question, use the graph in Figure 1 and the initial matching M = {(a, A), (b, B)}. A d B 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'|.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 22E

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