One way you might check to see whether a partial matching is maxi- mal is to construct an alternating path. This is a sequence of adjacent edges, which alternate between edges in the matching and edges not in the matching (no edge can be used more than once). If an alternat- ing path starts and stops with an edge not in the matching, then it is called an augmenting path.

One way you might check to see whether a partial matching is maxi- mal is to construct an alternating path. This is a sequence of adjacent edges, which alternate between edges in the matching and edges not in the matching (no edge can be used more than once). If an alternat- ing path starts and stops with an edge not in the matching, then it is called an augmenting path.

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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3. One way you might check to see whether a partial matching is maxi-
mal is to construct an alternating path. This is a sequence of adjacent
edges, which alternate between edges in the matching and edges not
in the matching (no edge can be used more than once). If an alternat-
ing path starts and stops with an edge not in the matching, then it is
called an augmenting path.
(a) Find the largest possible alternating path for the partial match-
ing of your friend's graph. Is it an augmenting path? How
would this help you find a larger matching?
(b) Find the largest possible alternating path for the partial match-
ing below. Are there any augmenting paths? Is the partial
matching the largest one that exists in the graph?

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