Partial Order
المؤلف:
Ruskey, F.
المصدر:
"Information on Linear Extension." http://www.theory.csc.uvic.ca/~cos/inf/pose/LinearExt.html.
الجزء والصفحة:
...
9-1-2022
1397
Partial Order
A relation "
" is a partial order on a set 
if it has:
1. Reflexivity: 
for all 
.
2. Antisymmetry: 
and 
implies 
.
3. Transitivity: 
and 
implies 
.
For a partial order, the size of the longest chain (antichain) is called the partial order length (partial order width). A partially ordered set is also called a poset.
A largest set of unrelated vertices in a partial order can be found using MaximumAntichain[g] in the Wolfram Language package Combinatorica` . MinimumChainPartition[g] in the Wolfram Language package Combinatorica` partitions a partial order into a minimum number of chains.
REFERENCES:
Ruskey, F. "Information on Linear Extension." http://www.theory.csc.uvic.ca/~cos/inf/pose/LinearExt.html.
Skiena, S. "Partial Orders." §5.4 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 203-209, 1990.
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