Publication details
THE LAST FRACTION OF A FRACTIONAL CONJECTURE
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | SIAM Journal on Discrete Mathematics |
| Citation | |
| Doi | https://doi.org/10.1137/090779097 |
| Keywords | fractional coloring; total coloring; girth |
| Description | Reed conjectured that for every epsilon > 0 and every integer Delta, there exists g such that the fractional total chromatic number of every graph with maximum degree Delta and girth at least g is at most Delta + 1 + epsilon. The conjecture was proven to be true when Delta = 3 or Delta is even. We settle the conjecture by proving it for the remaining cases. |