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Anderson and Lipman defined the wreath product and conjectured that the edge-chromatic number of GρH is of class 1 if G is of class 1. In the same paper, they asked about the edge-chromatic number of GρP2 and they hinted that this is probably difficult where P2 is a path of order 2. In this paper we prove that GρP2 is of class 1 for any graph G and prove that GρH is of class 1 if G is of class 1 and...
It is known that for any closed surface F2, every embedding on F2 with sufficiently large representativity is 5-colorable. In this paper, we shall characterize the 5-chromatic even triangulations on the Klein bottle with high representativity.
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