On Goldberg's Conjecture
by
Oguz Kurt
Ohio State University

In early 1970s, Goldberg conjectured that a multigraph G with chromatic index c' > D+1 satisfies c'=⌈c'^*⌉ where c'^* is the fractional chromatic index of G. Since Tashkinov showed that there exists an elementary and closed set X ⊂ V(G), the Kempe chain approach to this problem has been more and more active. Recently, we have shown that the conjecture holds if c' > [17/16]D+[14/16] or if c' > D+√{D/4}. Linearly and asymptotically, they are currently the best known results.

Date received: April 24, 2009