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