   # Edge Coloring In this section, we colored vertices of graphs so that no edge connected two vertices of the same color. We can also consider coloring edges, rather than vertices, so that no vertex connects two or more edges of the same color. In parts a to d, assign each edge in the graph a color so that no vertex connects two or more edges of the same color. Use the fewest number of colors possible. e. Explain why the number of colors required will always be at least the number of edges that meet at the vertex of highest degree in the graph. ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.4, Problem 30ES
Textbook Problem
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## Edge Coloring In this section, we colored vertices of graphs so that no edge connected two vertices of the same color. We can also consider coloring edges, rather than vertices, so that no vertex connects two or more edges of the same color. In parts a to d, assign each edge in the graph a color so that no vertex connects two or more edges of the same color. Use the fewest number of colors possible. e. Explain why the number of colors required will always be at least the number of edges that meet at the vertex of highest degree in the graph.

To determine

(a)

To draw:

A graph by assigning ach edge a color therefore no vertex connects two or more edges of same color.

### Explanation of Solution

Given:

Calculation:

Consider the given graph,

To determine

(b)

To draw:

A graph by assigning ach edge a color therefore no vertex connects two or more edges of same color.

To determine

(c)

To draw:

A graph by assigning ach edge a color therefore no vertex connects two or more edges of same color.

To determine

(d)

The graph with no vertex connects two or more edges of same color is drawn assigning each edge a color in the graph.

To determine

(e)

To draw:

A graph by assigning ach edge a color therefore no vertex connects two or more edges of same color.

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