Homework 7 Solutions
Basic Problems
1. In the graph BELOW on the LEFT, find 6 independent vertices, and 4 independent edges.
Explain how you can be certain that these sets are maximal without searching for larger
independent sets.
#1
#2
Answer:
Because +
Homework 5 Solutions
Basic Problems
1. Find and list all bridges of G.
Answer: qr, tw
2. Find and list all cut-vertices of G.
Answer: r, t, w
s
r
3. Find and draw all blocks of G.
Answer: Picture is shown below on the right.
x
w
t
x
y
q
s
v
u
r
z
r
q
G
w
Homework 9 Solutions
Basic Problems
1. Find a minimal proper vertex coloring for the graph below on the LEFT.
2. Find a minimal proper vertex coloring for the graph below on the RIGHT.
Answer:
Both graphs have = 3
3. Apply the Upper Bound Algorithm to the
Homework 1 Solutions
Basic Problems
1. Draw a visual representation of the graphthat has vertex set cfw_A, B, C, D, E and edge set
cfw_E, A, cfw_D, B, cfw_D, C, cfw_B, E, cfw_A, C, cfw_A, B.
Answer:
A
C
B
D
E
2. Draw a graph with of order 7 and size 6 tha
Homework 4
(Due at start of class on Thursday, Feb 25th)
Basic Problems
1. Draw all trees with degree sequence (3, 2, 2, 2, 1, 1, 1).
Answer:
2. Draw all trees of order 6 that have exactly one vertex whose degree is larger than 2.
Answer:
3. Suppose that
Math 3322
Spring 2014
Test 1
Name_
Due: Tuesday, February 25, 2014 at 11:59 pm
Show all work for full credit. Neatly and clearly indicate your answers. Remember, all
answers should be in complete sentences with explanations provided. You may work
with oth
Math 3322
Fall 2012
Test 2
Name_KEY_
Show all work for full credit. Neatly and clearly indicate your answers. Remember, all
answers should be in complete sentences with explanations provided. The only
exception is a graph.
1. How many license plates can b
Math 3322
Fall 2012
Test 3
Name_KEY_
Show all work for full credit. Neatly and clearly indicate your answers. Remember, all answers
should be in complete sentences with explanations provided. The only exception is a graph.
1. Explain how a combinatorial p
Math 3322
Fall 2011
Test 1
Name_KEY_
Show all work for full credit. Neatly and clearly indicate your answers. Remember, all
answers should be in complete sentences with explanations provided. The only
exception is a graph.
1. Discuss the difference betwee
Homework 3 Solutions
Basic Problems
1. (a) Starting with C4 , add a vertex to produce a graph having the degree sequence (3,3,3,3,2).
(b) Next add a vertex to produce a graph having the degree sequence (4,4,4,4,3,3).
(c) Finally add one more vertex to pro