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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

DM - Grand Test -Q11


Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
+1 vote

Which edge or pair of edges below CANNOT be extended to obtain a maximum cardinality matching for this graph? This is, which edge or pair of edges does NOT form a proper subset of a maximum cardinality matching?

               

(A) (I, J)

(B) (A, B) and (K, L)

(C) (C, D) and (J, K)

(D) (D, E) and (J, K)

asked Aug 30, 2020 by gbeditor-2 (72,840 points)
edited Sep 9, 2020 by deepak-gatebook

1 Answer

0 votes
 
Best answer
Matching in Graphs :

Let G be a graph. Two edges are independent if they have no common endvertex. A set M of independent edges of G is called a matching. The matching number, denoted µ(G), is the maximum size of a matching in G.

http://www-sop.inria.fr/members/Frederic.Havet/Cours/matching.pdf

For this given graph, we have a perfect matching that is of size 6. So, maximum cardinality of matching is 6.

Consider option C :

If you take  (C, D) and (J, K) in the matching then you cannot make 6 cardinality matching. At most 5 cardinality matching we can make.
answered Sep 9, 2020 by deepak-gatebook (226,240 points)
Answer:

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