Let G be a graph with possible multiple edges but no loops. The density of G, denoted by rho(G) , is defined as max(H subset of G, vertical bar V(H)vertical bar >= 2) inverted right perpendicular vertical bar E(H)vertical bar/left perpendicular vertical bar V(H)vertical bar/2 right perpendicular inverted left perpendicular. Goldberg (1973) and Seymour (1974) independently conjectured that if the chromatic index chi'(G) satisfies chi'(G) >= Delta(G) + 2 then chi'(G) = rho(G), which is commonly regarded as Goldberg's conjecture. An equivalent conjecture, usually credited to Jakobsen, states that...
