# Recent activity by ashutoshsharma

1
Let G be a connected 3 - regular graph. Each edge of G lies on some cycle. Let S⊆V and C1,C2,…,Cm,m=Codd(G−S), be the odd component of G−S. Let eG(Ci,S) denote the number of edges with one- end in Ci and the other in S. Then ∑(i=1 to m) eG(Ci−S) is (1) ≤m (2) ≥5m (3) ≥3m
2
Consider the preferences given in this Problem Student 1 2 3 4 University 1 2 3 4 A d a b c a C D B A B c b a d b D C A B C c b a d c A C B D D d a b c d B D A C The University - oriented stable matching obtained using Gale-Shapely Algorithm is (1) {aD,bc,cA,dB} (2) {aC,bD,cA,dB} (3) None of the above
3
Student 1 2 3 4 University 1 2 3 4 A d a b c a C D B A B c b a d b D C A B C c b a d c A C B D D d a b c d B D A C The Student - oriented stable matching obtained using Gale - Shapely Algorithm is (1) {Aa,Bb,Cc,Dd} (2) {Ac,Ba,Cb,Dd} (3) {Ac,Bd,Cb,Da} (4) None of the above
4
Consider the preferences Student 1 2 3 4 University 1 2 3 4 A d a b c a C D B A B c b a d b D C A B C c b a d c A C B D D d a b c d B D A C Is the matching M= {Ab,Ba,Cc,Dd} stable? (A) Yes (B) No
5
Let G be a connected 3 - regular graph. Each edge of G lies on some cycle. Let S⊆V and C1,C2,…,Cm,m=Codd(G−S), be the odd component of G−S. Let eG(Ci,S) denote the number of edges with one- end in Ci and the other in S. Then eG(Ci,S) is (A) Even (B) Odd (C) Cannot say
6
Determine whether the graph below has a perfect matching: (A) Yes (B) No
7
Determine whether the graph below has a perfect matching: (A) Yes (B) No
8
What is the size of minimum vertex cover for the graph G
9
In the above graph, find a maximum matching M. Then |M| is
10
Let T be a tree with n vertices and k be the maximum size of an independent set in T. Then the size of maximum matching in T is (A) k (B) n−k (C) (n−1)/2