Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Question
Chapter 34.5, Problem 1E
Program Plan Intro
To demonstrate that the sub-graph isomorphism problem is NP-complete.
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Students have asked these similar questions
4. The subgraph-isomorphism problem takes two graphs Gl and G2 and asks whether
Gl is isomorphic to a subgraph of G2. Show that
a) the subgraph-isomorphism problem is in NP; and
b) it is NP-complete by giving a polynomial time reduction from SAT problem to it.
Note: Two graphs G1=(V1, E1) and G2=(V2, E2) are isomorphic if there exists a one-
one and onto function f( ) from V1 to V2 such that for every two nodes u and v in V1,
(u,v) is in El if and only if (f(u), f(v)) is in E2. For examples, Gl is isomorphic to a
subgraph with vertices {1,2,5,4} of G2 below.
G1
G2
1
2
1
2
3
4
5
4
3
The subgraph-isomorphism problem takes two graphs G1 and G2 and asks
whether G1 is isomorphic to a subgraph of G2. Show that
a) the subgraph-isomorphism problem is in NP;
b) it is NP-complete by giving a polynomial time reduction from SAT problem to it.
and
Note: Two graphs G1=(V1, E1) and G2=(V2, E2) are isomorphic if there exists a
one-one and onto function f() from V1 to V2 such that for every two nodes u and
v in V1, (u.v) is in E1 if and only if (f(u), f(v)) is in E2. For examples, G1 is
isomorphic to a subgraph with vertices {1,2,5,4} of G2 below.
G1
G2
1
1
2
4
5
4
3.
2.
3.
For each pair of graphs G1 = <V1, E1> and G2 = <V2, E2>
a) determine if they are isomorphic or not.
b) Determine a function that can be isomorphic between them if they are isomorphic. Otherwise you should justify why they are not isomorphic.
c) is there an Euler road or an Euler bike in anyone graph? Is Hamilton available? You should draw if the answer is yes and reason if your answer is no.
Chapter 34 Solutions
Introduction to Algorithms
Ch. 34.1 - Prob. 1ECh. 34.1 - Prob. 2ECh. 34.1 - Prob. 3ECh. 34.1 - Prob. 4ECh. 34.1 - Prob. 5ECh. 34.1 - Prob. 6ECh. 34.2 - Prob. 1ECh. 34.2 - Prob. 2ECh. 34.2 - Prob. 3ECh. 34.2 - Prob. 4E
Ch. 34.2 - Prob. 5ECh. 34.2 - Prob. 6ECh. 34.2 - Prob. 7ECh. 34.2 - Prob. 8ECh. 34.2 - Prob. 9ECh. 34.2 - Prob. 10ECh. 34.2 - Prob. 11ECh. 34.3 - Prob. 1ECh. 34.3 - Prob. 2ECh. 34.3 - Prob. 3ECh. 34.3 - Prob. 4ECh. 34.3 - Prob. 5ECh. 34.3 - Prob. 6ECh. 34.3 - Prob. 7ECh. 34.3 - Prob. 8ECh. 34.4 - Prob. 1ECh. 34.4 - Prob. 2ECh. 34.4 - Prob. 3ECh. 34.4 - Prob. 4ECh. 34.4 - Prob. 5ECh. 34.4 - Prob. 6ECh. 34.4 - Prob. 7ECh. 34.5 - Prob. 1ECh. 34.5 - Prob. 2ECh. 34.5 - Prob. 3ECh. 34.5 - Prob. 4ECh. 34.5 - Prob. 5ECh. 34.5 - Prob. 6ECh. 34.5 - Prob. 7ECh. 34.5 - Prob. 8ECh. 34 - Prob. 1PCh. 34 - Prob. 2PCh. 34 - Prob. 3PCh. 34 - Prob. 4P
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