For a graph G=(V,E) and a color set C, let f:E→C be an edge-coloring of G in which two adjacent edges may have the same color. Then, the graph G edge-colored by f is rainbow connected if every two vertices of G have a path in which all edges are assigned distinct colors. Chakraborty et al. defined the problem of determining whether the graph colored by a… (More)
We construct, using multiple-scale analysis, a formal solution containing sufficiently many free parameters for the first Painlevé hierarchy (P I) m with a large parameter. This note is a short summary of our forthcoming paper .