15-344/Homework Assignment 5 - Revision history

Drorbn at 14:45, 3 November 2015

2015-11-03T14:45:51Z

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	'''Question by a student.''' For the additional problem: How can the vertices themselves be the trees without adding edges?		'''Question by a student.''' For the additional problem: How can the vertices themselves be the trees without adding edges?

	'''Answer.''' The vertices of a graph ~~may~~ be an arbitrary set. A set of apples, or of oranges, or of numbers, or of letters, or of spanning trees in another graph. In other words, for every spanning tree of the graph <math>G</math>, there's a vertex in the graph <math>\Gamma</math>. If <math>G</math> has 125 spanning trees, say, then <math>\Gamma</math> would have 125 vertices. --[[User:Drorbn\|Drorbn]] ([[User talk:Drorbn\|talk]]) 09:44, 3 November 2015 (EST)		'''Answer.''' The vertices of a graph can be an arbitrary set. A set of apples, or of oranges, or of numbers, or of letters, or of spanning trees in another graph. In other words, for every spanning tree of the graph <math>G</math>, there's a vertex in the graph <math>\Gamma</math>. If <math>G</math> has 125 spanning trees, say, then <math>\Gamma</math> would have 125 vertices. --[[User:Drorbn\|Drorbn]] ([[User talk:Drorbn\|talk]]) 09:44, 3 November 2015 (EST)

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Drorbn at 14:44, 3 November 2015

2015-11-03T14:44:28Z

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	Sorry for the delay with the preparation of this assignment!		Sorry for the delay with the preparation of this assignment!

			'''Question by a student.''' For the additional problem: How can the vertices themselves be the trees without adding edges?

			'''Answer.''' The vertices of a graph may be an arbitrary set. A set of apples, or of oranges, or of numbers, or of letters, or of spanning trees in another graph. In other words, for every spanning tree of the graph <math>G</math>, there's a vertex in the graph <math>\Gamma</math>. If <math>G</math> has 125 spanning trees, say, then <math>\Gamma</math> would have 125 vertices. --[[User:Drorbn\|Drorbn]] ([[User talk:Drorbn\|talk]]) 09:44, 3 November 2015 (EST)

	{{15-344:Dror/Students Divider}}		{{15-344:Dror/Students Divider}}

Drorbn at 23:11, 30 October 2015

2015-10-30T23:11:57Z

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	{{15-344/Navigation}}		{{15-344/Navigation}}
	{{In Preparation}}
	This assignment is due <span style="color: blue;">at the tutorials on Thursday November 5</span>. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.		This assignment is due <span style="color: blue;">at the tutorials on Thursday November 5</span>. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.

	'''Reread''' sections 4.1-4.2 of our textbook. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, '''preread''' chapter 5, just to get a feel for the future.		'''Reread''' sections 4.1-4.2 of our textbook. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, '''preread''' chapter 5, just to get a feel for the future.

	'''Solve''' problems ... in section ... but submit only your solutions of the underlined problems.		'''Solve''' problems 3, 5, 7, and <u>15</u> in section 3.1, problems 1 and <u>9</u> in section 4.1, and problems 1 and 12 in section 4.2, but submit only your solutions of the underlined problems. In addition, solve and submit the following

			'''Additional Problem.''' Given a connected graph <math>G</math>, let <math>\Gamma</math> be the graph whose vertices are the spanning trees of <math>G</math>, and where two vertices <math>T</math> and <math>T'</math> in <math>\Gamma</math> are connected by an edge in <math>\Gamma</math> if <math>T'</math> is obtained from <math>T</math> by removing one edge and adding one edge. Prove that <math>\Gamma</math> is itself a connected graph.

			Sorry for the delay with the preparation of this assignment!

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Drorbn: Created page with "{{15-344/Navigation}} {{In Preparation}} This assignment is due at the tutorials on Thursday November 5. Here and everywhere, '''neatness cou..."

2015-10-29T13:46:52Z

Created page with "{{15-344/Navigation}} {{In Preparation}} This assignment is due <span style="color: blue;">at the tutorials on Thursday November 5</span>. Here and everywhere, '''neatness cou..."

New page

{{15-344/Navigation}}
{{In Preparation}}
This assignment is due <span style="color: blue;">at the tutorials on Thursday November 5</span>. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.

'''Reread''' sections 4.1-4.2 of our textbook. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, '''preread''' chapter 5, just to get a feel for the future.

'''Solve''' problems ... in section ... but submit only your solutions of the underlined problems.

{{15-344:Dror/Students Divider}}