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:
“Religious literature has eminent examples, and if we run over our private list of poets, critics, philanthropists and philosophers, we shall find them infected with this dropsy and elephantiasis, which we ought to have tapped.”
—Ralph Waldo Emerson (1803–1882)
“What these perplexities of my uncle Toby were,—’tis impossible for you to guess;Mif you could,—I should blush ... as an author; inasmuch as I set no small store by myself upon this very account, that my reader has never yet been able to guess at any thing. And ... if I thought you was able to form the least ... conjecture to yourself, of what was to come in the next page,—I would tear it out of my book.”
—Laurence Sterne (1713–1768)