Each of the following problems can be solved by finding either the chromatic number of a graph or the chromatic index of a graph. For each problem, say whether you should find a proper coloring of the vertices or of the edges of the graph to solve the problem. Note: you likely don't have enough information to actually solve the problem, but this is okay. Just say in principle whether this is an edge-coloring or vertex-coloring application. ? 1. At a speed dating event, everyone must spend 5 minutes talking to another person before moving on to the next. How long must the event be? ? 2. At the world Tic-Tac-Toe championship, each player must play against 7 other players. New games start every hour. How many hours will the tournament take? ? 3. The math department wants to schedule common, day-long midterm exams over Spring Break, but obviously a student in two classes has to have their exams for those classes on different days (but this is the only problem with this plan). How many days are needed for exams? ? 4. Professor Snape stores potion ingrediants in as few cabinates as possible, but some ingrediants can't be stored in the same cabinate because they could interact dangerously. How many cabinates are required?
Each of the following problems can be solved by finding either the chromatic number of a graph or the chromatic index of a graph. For each problem, say whether you should find a proper coloring of the vertices or of the edges of the graph to solve the problem. Note: you likely don't have enough information to actually solve the problem, but this is okay. Just say in principle whether this is an edge-coloring or vertex-coloring application. ? 1. At a speed dating event, everyone must spend 5 minutes talking to another person before moving on to the next. How long must the event be? ? 2. At the world Tic-Tac-Toe championship, each player must play against 7 other players. New games start every hour. How many hours will the tournament take? ? 3. The math department wants to schedule common, day-long midterm exams over Spring Break, but obviously a student in two classes has to have their exams for those classes on different days (but this is the only problem with this plan). How many days are needed for exams? ? 4. Professor Snape stores potion ingrediants in as few cabinates as possible, but some ingrediants can't be stored in the same cabinate because they could interact dangerously. How many cabinates are required?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Each of the following problems can be solved by finding either the chromatic number of a graph or the chromatic index of a graph.
For each problem, say whether you should find a proper coloring of the vertices or of the edges of the graph to solve the problem. Note: you
likely don't have enough information to actually solve the problem, but this is okay. Just say in principle whether this is an edge-coloring or
vertex-coloring application.
?
1. At a speed dating event, everyone must spend 5 minutes talking to another person before moving on to the next. How
long must the event be?
?
2. At the world Tic-Tac-Toe championship, each player must play against 7 other players. New games start every hour. How
many hours will the tournament take?
?
3. The math department wants to schedule common, day-long midterm exams over Spring Break, but obviously a student in
two classes has to have their exams for those classes on different days (but this is the only problem with this plan). How many days are
needed for exams?
?
4. Professor Snape stores potion ingrediants in as few cabinates as possible, but some ingrediants can't be stored in the
same cabinate because they could interact dangerously. How many cabinates are required?
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