MTH 325: Guided Practice 13
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Exercises for this Guided Practice
Please work out your answers to these exercises separately (on paper or in a text file) and then put your answers for each one below. You will receive a PASS grade on this assignment if each of the following exercises is completed with a goodfaith effort to be right, and if this form is submitted before the 11:59pm deadline on the day it's due (check the calendar for specific dates). Correctness is NOT part of the grade, although some questions will show you correct answers once you submit the form.
(REVIEW) Suppose that a graph G has an Euler circuit. Which of the following can we conclude about it? Select all that apply.
The graph has exactly two vertices with odd degree.
The graph has exactly zero vertices with odd degree.
The graph has an even, but not necessarily zero number of vertices with odd degree.
The graph also has an Euler path (that is not a circuit).
We cannot conclude any of the above based only on this information.
(SYLLABUS) What are the Learning Targets covered on Quiz 3?
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The "problem set" at the end of the video in the Guided Practice asks you to think about whether/why the complete bipartite graph K_{m,n} is Hamiltonian. Here is a picture of K_{3,4}. Is it Hamiltonian? If it is, give a Hamilton path as a sequence of vertices. Otherwise explain what happened as you tried to find a Hamilton path.
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Now consider K_{4,4} below. Is this one Hamiltonian? Again if you believe it is Hamiltonian, then find a Hamilton path in it and state it as a sequence of vertices. Otherwise explain what happened as you tried to find a Hamilton path.
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What possible uses could Hamilton paths have in computer science or in practical applications?
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What specific questions do you have about this lesson so far? (For questions about the course, grading, etc. please email those and do not include them here.)
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