Talk:Mycielskian

Afaik the generalized construction mentioned in the second paragraph goes back to: Claude Tardif. Fractional chromatic numbers of cones over graphs. J. Graph Theory, 38(2):87–94, 2001 130.149.15.195 (talk) 16:09, 26 June 2009 (UTC)[reply]

Fixed, I think. Tardif's paper seems to be giving credit for the construction to a 1985 thesis of Stiebitz. —David Eppstein (talk) 19:57, 26 June 2009 (UTC)[reply]

There may be a problem with the definition of Generalized Mycielskian. In the case of a disconnected graph G, the tensor product of G with the path graph of length 2 with a loop at one end, is not the same graph as the Mycielskian of G. — Preceding unsigned comment added by Oglem (talk • contribs) 15:40, 6 May 2021 (UTC)[reply]

For the proof of the chromatic number, if G is connected I don't believe we could recolor any vertex since the coloring would no longer be proper. Of course if G is connected with n + 1 vertices, it trivially has chromatic number k + 1. Calabimanicure (talk) 02:49, 20 March 2022 (UTC)[reply]