ON THE COLORABILITY OF M-COMPOSED GRAPHS

A graph is called m-degenerated if each of its subgraphs has minimum degree at most m. A graph, which is the union of an m-degenerated graph and an acyclic graph is called m-composed. Such a graph is (2m + 2)-colorable. Here it is conjectured that such a graph is nu = m + 1 + left-perpendicular (1 + square-root 8m + 1)/2 right-perpendicular-colorable. In support of this, wide classes of (nu + 1)-chromatic graphs are shown not to be m-composed. The conjecture for m = 2 is an open problem of Tarsi.