Assignment 2 – Part A
CPS 420
W2017
1. Please fill out the following table as explained on the assignment page. Kn is a complete graph
with n vertices.
K graph
Euler circuit
Hamiltonian circuit
K1
1
K2
1
K3
2
1
K4
3
2
1
2
4
3
K5
1
5
2
4
K6
3
1
6
2
5
3
4
Page | 1
Assignment 2 – Part A
CPS 420
W2017
2. Please fill out the following table as explained on the assignment page. Kn,m is a complete bipartite
graph of n vertices between a set of n vertices and a set of m vertices.
K graph
Euler circuit
Hamiltonian circuit
K1,1
1
a
K1,2
1
a
b
1
2
a
b
K2,2
K1,3
1
a
c
b
K2,3
1
a
2
b
c
Page | 2
Assignment 2 – Part A
CPS 420
K graph
Euler circuit
W2017
Hamiltonian circuit
K3,3
1
2
3
a
b
c
K3,4
1
3
2
a
b
c
d
1
2
3
4
a
b
c
d
K4,4
3. Give a simple rule to describe for which values of n Kn has an Euler circuit and when it does not.
Explain why your rule is valid.
Page | 3
CPS 420
Assignment 2 – Part A
W2017
4. Give a simple rule to describe for which values of n Kn has a Hamiltonian circuit and when it does
not. Explain why your rule is valid.
5. Give a simple rule to describe for which values of n and m Kn,m has an Euler circuit and when it
does not. Explain why your rule is valid.
6. Give a simple rule to describe for which values of n and m Kn,m has a Hamiltonian circuit and when
it does not. Explain why your rule is valid.
Page | 4