Talk:Brooks' theorem

Hello, I don't understand why my contribution has been removed. In the page on Grötzsch's theorem it is stated clearly (my own contribution) that a planar graph not containing K_4 and still not 4-colorable exists. Since an example (not found by me) is available, namely http://math.asu.edu/~checkman/steinberg5cycle.jpg, i do not understand what exactly is disputable here. Delio.mugnolo (talk) 09:35, 31 December 2010 (UTC)[reply]

What does this have to do with graphs of maximum degree Δ? Your example has no K_4, but its maximum degree is 5? In any case a much simpler counterexample to the removed statement (for small Δ) is possible: the pentagonal prism has Δ=3, is triangle-free, but requires three colors instead of only two. —David Eppstein (talk) 17:59, 31 December 2010 (UTC)[reply]

Sorry, you are right. —Delio.mugnolo (talk) 14:11, 1 January 2011 (UTC)[reply]