Every graph's list chromatic index equals its chromatic index.
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Statement
For every multigraph $G$, $\chi'_{\ell}(G) = \chi'(G)$: edges are list-colorable from any lists of size $\chi'(G)$ (List Edge Coloring Conjecture).
Assessment
Renown 3/5
The Dinitz problem (its Latin-square case, proved by Galvin) made it famous; the general statement remains open.
Attackability 1/5
Counterexample requires exhibiting lists with no proper coloring -- a co-NP-flavored certificate that is exponentially expensive to verify; proved for bipartite (Galvin) and planar cubic classes.
- finite witness
- 3/5
- oracle cost
- 1/5
- freshness
- 1/5
- seedability
- 1/5
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
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Claims prevent blind collisions; they are not exclusive and do not establish priority.