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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.1, Problem 28ES

Textbook Problem

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Transportation A subway map is shown below. Is it possible for a rider to travel the length of every subway route without repeating any segments? Justify your conclusion.

To determine

To determine if it is possible for a rider to travel the length of every subway route without repeating any segments.

**Given information:**

Given, a subway map below to check if it is possible for a rider to travel the length of every subway route without repeating any segments.

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**Calculation:**

To check the possibility of the travel, the arrangement is to be graphed.

Every intersection is considered (since most of the subways are on single route) as a vertex and every route is considered an edge as shown below:

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Using the above image, the graph can be made as:

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It is possible for a rider to travel the length of every subway route without repeating any segments if the graph satisfies the condition of either Euler circuit or Euler path.

An Eulerian graph (that starts and ends at the same vertex) is said to be Euler circuit if it uses every edge, but only once. (i.e. no edge is used more than once).

Euler path is defined as the path in a connected graph that has exactly two vertices of odd degree with all the remaining vertices of even degree and the path starts at one of the vertices with odd degree and ends at the other vertex with odd degree...

Mathematical Excursions (MindTap Course List)

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Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - Explain why the following pen-tracing puzzle is...Ch. 5.1 - Transportation An X in the table below indicates a...Ch. 5.1 - Transportation The table below shows the nonstop...Ch. 5.1 - Social Network A group of friends is represented...Ch. 5.1 - Baseball The local Little League baseball teams...Ch. 5.1 - Determine (a) the number of edges in the graph,...

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The...Ch. 5.4 - A one-way road intersects a two-way road in a...Ch. 5.4 - A two-way road intersects another two-way road in...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Scheduling Six student clubs need to hold meetings...Ch. 5.4 - Scheduling Eight political committees must meet on...Ch. 5.4 - Scheduling Six different groups of children would...Ch. 5.4 - Scheduling Five different charity organizations...Ch. 5.4 - Scheduling Students in a film class have...Ch. 5.4 - Animal Housing A researcher has discovered six new...Ch. 5.4 - Wi-Fi Stations An office building is installing...Ch. 5.4 - Map Coloring Draw a map of a fictional continent...Ch. 5.4 - If the chromatic number of a graph with five...Ch. 5.4 - Edge Coloring In this section, we colored vertices...Ch. 5.4 - Scheduling Edge colorings, as explained in...Ch. 5 - (a) determine the number of edges in the graph,...Ch. 5 - (a) determine the number of edges in the graph,...Ch. 5 - Soccer In the table below, an X indicates teams...Ch. 5 - Each vertex in the graph at the left represents a...Ch. 5 - Determine whether the two graphs are equivalent.Ch. 5 - Determine whether the two graphs are equivalent.Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Parks The figure shows an arrangement of bridges...Ch. 5 - Architecture The floor plan of a sculpture gallery...Ch. 5 - Use Dirac's theorem to verify that the graph is...Ch. 5 - Use Dirac's theorem to verify that the graph is...Ch. 5 - Travel The table below lists cities serviced by a...Ch. 5 - Travel For the direct flights given in Exercise...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Use the edge-picking algorithm to find a...Ch. 5 - Use the edge-picking algorithm to find a...Ch. 5 - Efficient Route The distances, in miles, between...Ch. 5 - Computer Networking A small office needs to...Ch. 5 - Show that the graphs is planar by finding a planar...Ch. 5 - Show that the graphs is planar by finding a planar...Ch. 5 - Show that the graph is not planar.Ch. 5 - Show that the graph is not planar.Ch. 5 - Count the number of vertices, edges, and faces in...Ch. 5 - Count the number of vertices, edges, and faces in...Ch. 5 - Map Coloring, a fictional map is given showing the...Ch. 5 - Map Coloring, a fictional map is given showing the...Ch. 5 - Show that the graph is 2-colorable by finding a...Ch. 5 - Show that the graph is 2-colorable by finding a...Ch. 5 - Determine (by trial and error) the chromatic...Ch. 5 - Determine (by trial and error) the chromatic...Ch. 5 - Scheduling A company has scheduled a retreat at a...Ch. 5 - Social Network Each vertex in the graph at the...Ch. 5 - Determine whether the following two graphs are...Ch. 5 - Answer the following questions for the graph shown...Ch. 5 - Recreation The illustration below depicts bridges...Ch. 5 - a. 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