From ping.zhang@wmich.edu Fri Oct 08 13:54:44 2004
Date: Fri, 08 Oct 2004 13:56:41 -0400
From: Ping Zhang <ping.zhang@wmich.edu>
To: David Ritter <ritterd@fiu.edu>
Subject: Re: Intro to Graph Theory: Problem 2.12

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Dear Professor Ritter:

Thank you for your email!

 I will read your solution and get back to you soon.

Thank you again.

Best wishes, Ping

Ping Zhang
Department of Mathematics
Western Michigan University
Kalamazoo, MI 49008
Telephone  269-387-4730
Fax: 269-387-4530
Email: ping.zhang@wmich.edu
Web: http://homepages.wmich.edu/~zhang/




David Ritter wrote:

>Professors Chartrand and Zhang,
>
>This is probably one for the next edition.  I am using your text
>while teaching MAD3305, Graph Theory, at FIU.  I bumped into a small
>problem with Problem 2.12:
>
>"Prove that if G is a graph of order n such the
>
>	DELTA(G) + delta(G) >= n-1,
>
>then G is connected and diam(G) <= 2.  Show that the bound is sharp."
>
>After working on it for a while and essentially solving it, I went to
>Prof. Zhang's site and found amongst the "corrections" that the inequality
>concerning the upper bound on the diameter of the graph had been removed.
>Perhaps a better idea is to replace the "2" with a "4" and add a
>sentence:
>	Show that diam(G) <= 4 is also best possible.
>
>Attached, you'll find a pdf of my solution together with the few warts it
>has remaining.  I suspect the result must be "folk lore" but since I am
>not really a graph theorist, I am not on top of the matter.
>
>Regards,
>
>David
>
>David L. Ritter, Ph.D.
>Associate Professor
>Department of Mathematics
>F.I.U.
>University Park
>Miami, FL 33199
>  
>


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