|
|
| Line 1: |
Line 1: |
| In [[combinatorics]], the '''Dinitz conjecture''' is a statement about the extension of arrays to partial [[Latin squares]], proposed in 1979 by [[Jeff Dinitz]], and proved in 1994 by [[Fred Galvin]].
| |
|
| |
|
| The Dinitz conjecture, now a theorem, is that given an ''n'' × ''n'' square array, a set of ''m'' symbols with ''m'' ≥ ''n'', and for each cell of the array an ''n''-element set drawn from the pool of ''m'' symbols, it is possible to choose a way of labeling each cell with one of those elements in such a way that no row or column repeats a symbol.
| |
|
| |
|
| The Dinitz conjecture is closely related to [[graph theory]], in which it can be succinctly stated as <math>\chi^\prime_l(K_{n, n}) = n</math> for natural <math>n</math>. It means that the [[list chromatic index]] of the [[complete bipartite graph]] <math>K_{n, n}</math> equals <math>n</math>. In fact, Fred Galvin proved the Dinitz conjecture as a special case of his theorem stating that the list chromatic index of any bipartite multigraph is equal to its [[chromatic index]]. Moreover, it is also a special case of the '''edge list coloring conjecture''' saying that the same holds not only for bipartite graphs, but also for any loopless multigraph. | | The [http://www.tumblr.com/tagged/writer%27s writer's] name is Milford Wyant. Invoicing is how I make a residing and I don't believe I'll alter it whenever quickly. To perform domino is 1 of the things he loves most. He's usually loved living in Delaware and his parents live nearby. See what's new on her web site here: http://www.trachome.com/Nya_Online_Casino_Is_Essential_For_Your_Success._Read_This_To_Find_Out_Why<br><br>Feel free to visit my page; [http://www.trachome.com/Nya_Online_Casino_Is_Essential_For_Your_Success._Read_This_To_Find_Out_Why nya internet svenska casinon] |
| | |
| ==References==
| |
| * {{cite journal | author=F. Galvin | authorlink=Fred Galvin | title=The list chromatic index of a bipartite multigraph |journal=Journal of Combinatorial Theory |series=Series B |volume=63 |issue=1 |year=1995 |pages=153–158 |doi=10.1006/jctb.1995.1011}}
| |
| * {{cite journal |last=Zeilberger |first=D. |authorlink=Doron Zeilberger |coauthors= |year=1996 |month= |title=The Method of Undetermined Generalization and Specialization Illustrated with Fred Galvin's Amazing Proof of the Dinitz Conjecture |journal=The American mathematical monthly |volume=103 |issue=3 |pages=233–239 |id= |arxiv=math/9506215 }}
| |
| * {{cite journal |last=Chow |first=T. Y. |authorlink= |coauthors= |year=1995 |month= |title=On the Dinitz conjecture and related conjectures |journal=Discrete Math |volume=145 |issue= |pages=145–173 |id= |url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.72.7005 |accessdate=2009-04-15 |quote= }}
| |
| | |
| ==External links==
| |
| * {{MathWorld|title=Dinitz Problem|urlname=DinitzProblem|accessdate=2008-08-17}}
| |
| | |
| [[Category:Combinatorics]]
| |
| [[Category:Latin squares]]
| |
| [[Category:Graph coloring]]
| |
| [[Category:Theorems in discrete mathematics]]
| |
| | |
| | |
| {{combin-stub}}
| |
The writer's name is Milford Wyant. Invoicing is how I make a residing and I don't believe I'll alter it whenever quickly. To perform domino is 1 of the things he loves most. He's usually loved living in Delaware and his parents live nearby. See what's new on her web site here: http://www.trachome.com/Nya_Online_Casino_Is_Essential_For_Your_Success._Read_This_To_Find_Out_Why
Feel free to visit my page; nya internet svenska casinon