| ¡@¡@The edge-face chromatic number (G) of a plane graph G is the least number of colors needed to color simultanously the edges and faces of G such that any two adjacent or incident elements have different colors. In 1975, Melnikov conjectured that every plane graph G is (£G(G)+3)-edge-face colorable, where £G(G) denotes the maximum degree of G. In this talk we survey three independent proofs for this conjecture and give some new open prolems about the related area. We also generalize this result to the case of the edge-face list coloring of plane grapgs. |