Marc, Thanks for answering. The graphs I am concerned with are all connected. The path I want is called an Eulerian Cycle, according to Eric's Encyclopedia, which does not quite answer my question. Now if I can find my copy of Harary, the answer might be there. ----- Original Message ----- From: "Marc LeBrun" <mlb@fxpt.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Thursday, February 03, 2005 3:21 PM Subject: Re: [math-fun] Question about graphs
Neat question!
=Steve Gray An obvious threorem in simple graph theory says that no graph with (no) An extra negation may have slipped in here: (YOU'RE CORRECT) ^^ more than two nodes of odd order can be drawn in one continuous path. Is there a theorem saying that any graph with two, one, or zero nodes of odd order can always be drawn in one continuous path? A yes/no answer would be nice,
No, not without also requiring the graph to be connected.
and a reference would be even nicer.
I'll have to leave that to the professionals.
Thanks for any info.
"Enjoy"!
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