The most famous open problem about list edge-coloring is probably the list coloring conjecture.
- ch′(G) = χ′(G).
This conjecture has a fuzzy origin; Jensen & Toft (1995) overview its history. The Dinitz conjecture, proven by Galvin (1995), is the special case of the list coloring conjecture for the complete bipartite graphs Kn,n.
Read more about this topic: List Edge-coloring
Famous quotes containing the words list and/or conjecture:
“The advice of their elders to young men is very apt to be as unreal as a list of the hundred best books.”
—Oliver Wendell Holmes, Jr. (1841–1935)
“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)