Alon–Tarsi conjecture
E621147
The Alon–Tarsi conjecture is a prominent open problem in combinatorics and graph theory concerning orientations and colorings of graphs, with deep connections to Latin squares and polynomial method techniques.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Alon–Tarsi conjecture canonical | 1 |
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical conjecture
ⓘ
open problem in combinatorics ⓘ |
| conjecturedBy |
Michael Tarsi
NERFINISHED
ⓘ
Noga Alon NERFINISHED ⓘ |
| describedIn | paper by Noga Alon and Michael Tarsi on colorings and orientations of graphs ⓘ |
| field |
combinatorics
ⓘ
graph theory ⓘ |
| hasConnectionTo |
Latin squares
NERFINISHED
ⓘ
Tutte polynomial NERFINISHED ⓘ acyclic orientations ⓘ algebraic proof techniques in graph coloring ⓘ bipartite Eulerian orientations ⓘ coloring polynomial ⓘ combinatorial Nullstellensatz NERFINISHED ⓘ difference between numbers of even and odd Latin squares ⓘ even and odd orientations of graphs ⓘ graph choosability ⓘ graph polynomials ⓘ list coloring of graphs ⓘ orientation counting in graphs ⓘ parity arguments in combinatorics ⓘ parity of Latin squares ⓘ polynomial method ⓘ sign of permutations in Latin squares ⓘ |
| hasInfluenceOn |
development of algebraic methods in combinatorics
ⓘ
research on graph colorings via orientations ⓘ |
| hasVariant | Alon–Tarsi conjecture for Latin squares NERFINISHED ⓘ |
| implies | results on list colorings of planar graphs ⓘ |
| mainSubject |
graph colorings
ⓘ
graph orientations ⓘ |
| namedAfter |
Michael Tarsi
NERFINISHED
ⓘ
Noga Alon NERFINISHED ⓘ |
| relatedConjecture |
circular choosability conjecture
NERFINISHED
ⓘ
list coloring conjecture NERFINISHED ⓘ |
| relatesTo |
Eulerian subgraphs
ⓘ
bipartite graphs ⓘ chromatic number of graphs ⓘ complete bipartite graphs ⓘ list chromatic number ⓘ |
| status | open ⓘ |
| studiedIn |
algebraic graph theory
ⓘ
extremal combinatorics ⓘ |
| usedIn | applications of the combinatorial Nullstellensatz ⓘ |
| yearProposed | 1992 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.