From: utzoo!decvax!harpo!floyd!cmcl2!philabs!sdcsvax!sdchema!donn
Newsgroups: net.misc
Title: Hamilton Cycle of the Net?
Article-I.D.: sdchema.445
Posted: Sun Mar 13 02:30:21 1983
Received: Mon Mar 14 03:06:19 1983

Now that we have some better data on the topology of the net, thanks to
the efforts of various people such as Steven Bellovin, maybe we can
answer some silly trivia questions such as, what is the longest path on
the net?  Remember, news (unlike mail) never goes through the same
machine twice, so if there was a route that took you through every
machine on the net then it would be a Hamilton cycle (according to my
vague recollection of graph theory -- correct me if I'm wrong).  It's a
fairly simple undertaking to measure the longest path in one's current
batch of news so I did it on our local machine.  It turns out have 29
machines in it (the path is hyphenated for the benefit of those with
brain-damaged terminals):

    sdchema!sdcsvax!philabs!cmcl2!floyd!vax135!ariel!houti!lime-
	   !we13!otuxa!ll1!sb1!burl!mhuxv!mhuxm!mhuxh!mhuxa!mhuxt-
	   !eagle!harpo!seismo!hao!hplabs!sri-unix!cca!decvax-
	   !utzoo!utcsrgv!newman

Notice that it crosses the country from coast to coast at least three
times...  and ends up in Canada.  I guess the question I want to ask
is, what is the maximal subgraph of the net that has a Hamilton cycle?
I.e., what is the upper bound on the path length of a news item?

Donn Seeley  UCSD Chemistry Dept. RRCF  ucbvax!sdcsvax!sdchema!donn