This paper exploits the remarkable new method of Galvin (J. Combin. Theory Ser. B 63 (1995), 153 158), who proved that the list edge chromatic number /$list(G) of a bipartite multigraph G equals itsâ€¦ (More)

After a brief historical account, a few simple structural theorems about plane graphs useful for coloring are stated, and two simple applications of discharging are given. Afterwards, the followingâ€¦ (More)

We prove that every planar graph with maximum degree âˆ† is strong edge (2âˆ†âˆ’ 1)-colorable if its girth is at least 40âŒŠ 2 âŒ‹+1. The bound 2âˆ†âˆ’ 1 is reached at any graph that has two adjacent vertices ofâ€¦ (More)

Planar graphs without 3-cycles at distance less than 4 and without 5-cycles are proved to be 3-colorable. We conjecture that, moreover, each plane graph with neither 5-cycles nor intersectingâ€¦ (More)

We show that a planar graph with girth at least 20tâˆ’2 3 has circular chromatic number at most 2+ 1t , improving earlier results. This follows from a general result establishing homomorphisms intoâ€¦ (More)

The oriented chromatic number o(H) of an oriented graph H is de ned as the minimum order of an oriented graph H â€² such that H has a homomorphism to H â€². The oriented chromatic number o(G) of anâ€¦ (More)