Talk:Tietze's graph

Name origin[edit]

I wonder where the name 'Tietze' came from. Is it related to Heinrich Tietze? - Jochen Burghardt (talk) 07:31, 5 October 2014 (UTC)[reply]

arxiv:1309.6469 says yes, but without any convincing detail about why it's named after him, and there has also been work published in graph theory by someone else named Walter Tietze. So I'm hesitant to add this to the article until we can get a clearer answer. —David Eppstein (talk) 18:32, 5 October 2014 (UTC)[reply]

I copied (almost all of) the publication references from de.wikipedia for the Heinrich Tietze article. The 1910 one gives an example of a map on a Moebius strip that needs 6 colors; it looks somewhat similar to the Moebius image here (for a non-graphtheorist like me), but they are not quite the same, maybe dual (I remember to have seen this notion somewhere recently...) to each other. Probably, you can tell whether they could be related; I could help with translating small crucial article parts if necessary. - Jochen Burghardt (talk) 19:37, 5 October 2014 (UTC)[reply]

Yes, that must be it. If you take the Möbius map from the 1910 paper, and draw a graph whose edges are the boundaries of regions (either between two regions or along the boundary of the strip) then you get exactly Tietze's graph. This map is the one shown in the Möbius image, but I think it can be drawn more clearly using a three-dimensional embedding of the Möbius strip. —David Eppstein (talk) 19:57, 5 October 2014 (UTC)[reply]

Ok; it took me a while to see it - the wikipedia graph can be obtained by cutting the 1910 Moebius strip along the (suffiently extended) line between region 4 and 5. - Thanks for updating the article meanwhile! - Jochen Burghardt (talk) 20:16, 5 October 2014 (UTC)[reply]