Math 3116
Dr. Franz Rothe
June 24, 2013
Name:
08SUM\3116_2013t1.tex
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Solution of Test
Lemma 1 (Return lemma). In a graph all vertices of which have degree at least two, a
cycle exists.
10 Problem 1.1. Prove the Lemma.
Answer. One can continue a path unti
Math 3116
Dr. Franz Rothe
June 24, 2013
Name:
08SUM\3116_2013pr.tex
10 Problem 0.1. Calculate the currents and voltages for the electrical network
on page 1.
Figure 1: Calculate the currents and voltages.
Answer. I have used the rst-depth tree and the lab
Math 3116
Dr. Franz Rothe
June 18, 2012
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08SUM\3116_2012h3.tex
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3.1
Homework
Spanning trees, and so on
20 Problem 3.1. Given is a rooted K4 , with the vertices at the corners of square
a
Math 3181
Dr. Franz Rothe
August 28, 2013
Name:
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13FALL\4161_fall13r1.tex
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due in two weeks
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2.1
Homework
Binomial coecients with non-integer top
10 Problem 2.1. With z R or even z C, and
Math 3116
Dr. Franz Rothe
June 23, 2013
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08SUM\3116_2013h2.tex
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Homework
10 Problem 2.1. A polyhedra has 9 vertices and 7 faces. Five of the faces are
squares. Determine the lengths of the two remaining faces. Draw
Math 3116
Dr. Franz Rothe
July 24, 2012
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08SUM\3116_2012f.tex
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4.1
Final
Degree sequence
10 Problem 4.1. Use the reduction algorithm to nd a simple graph with degree
sequence
Math 3116
Dr. Franz Rothe
June 9, 2012
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08SUM\3116_2012h2.tex
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2.1
Homework
Taits conjecture
In his attempt to prove the Four Color Theorem, around 1878 Tait made the following
wro
Math 3116
Dr. Franz Rothe
June 23, 2013
Name:
08SUM\3116_2013h2.tex
2
Some Solution of Homework
10 Problem 2.1. A polyhedra has 9 vertices and 7 faces. Five of the faces are
squares. Determine the lengths of the two remaining faces. Draw the planar graph.
Math 3116
Dr. Franz Rothe
May 30, 2012
Name:
08SUM\3116_2012h1.tex
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1
Some Solution of Homework
Proposition 1 (Counting labeled trees). There are nn2 dierent labeled trees with
n vertices.
Corollary 1 (Spanning trees of t
Math 3116
Dr. Franz Rothe
June 4, 2012
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08SUM\3116_2012t1.tex
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1
1.1
Test
Eulerian graphs
Proposition 1. The edges of an even graph can be split (partitioned) into cycles, no
two of whic
Math 3116
Dr. Franz Rothe
June 23, 2013
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08SUM\3116_2013t1.tex
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Test
Lemma 1 (Return lemma). In a graph all vertices of which have degree at least two, a
cycle exists.
10 Problem 1.1. Prove the Lemma.
1
Denition 1.
Math 3116
Dr. Franz Rothe
June 5, 2012
Name:
08SUM\3116_2012t1.tex
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1
1.1
Solution of Test
Eulerian graphs
Proposition 1. The edges of an even graph can be split (partitioned) into cycles, no
two of which have an edge in
Math 3116
Dr. Franz Rothe
May 24, 2012
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08SUM\3116_2012h1.tex
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1
Homework
Proposition 1 (Counting labeled trees). There are nn2 dierent labeled trees with
n vertices.
Corollary 1 (S