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# minimal cut set fn (MinimalCutSetFn)

A UnaryFunction that assigns a Graph the Class of GraphPaths which comprise cutsets for the Graph and which have the least number of GraphArcs.

## Ontology

SUMO / GRAPH-THEORY

## Class(es)

 class

inheritable relation

unary function

minimal cut set fn

## Coordinate term(s)

absolute value fn  abstraction fn  arc cosine fn  arc sine fn  arc tangent fn  back fn  begin fn  begin node fn  cardinality fn  ceiling fn  complement fn  cosine fn  cut set fn  denominator fn  end fn  end node fn  extension fn  floor fn  front fn  future fn  generalized intersection fn  generalized union fn  giga fn  imaginary part fn  immediate future fn  immediate past fn  initial node fn  integer square root fn  kilo fn  list length fn  magnitude fn  mega fn  micro fn  milli fn  nano fn  numerator fn  organization fn  past fn  path weight fn  pico fn  power set fn  predecessor fn  principal host fn  probability fn  property fn  rational number fn  real number fn  reciprocal fn  round fn  signum fn  sine fn  skin fn  square root fn  successor fn  tangent fn  tera fn  terminal node fn  wealth fn  when fn  year fn

## Type restrictions

subclass graph path MinimalCutSetFn(graph)

## Axioms (4)

minimal cut set fn is internally related to cut set fn.
`(relatedInternalConcept MinimalCutSetFn CutSetFn)`

If graph is an instance of graph, then "the set of minimal paths that partition graph into two separate graphs" is a subclass of "the set of paths that partition graph into two separate graphs".
```(=>
(instance ?GRAPH Graph)
(subclass
(MinimalCutSetFn ?GRAPH)
(CutSetFn ?GRAPH)))```

• if "the set of minimal paths that partition graph into two separate graphs" is equal to pathclass,
• then there exists number so that for all path holds: if path is an instance of pathclass, then the length of path is number
• .
```(=>
(equal
(MinimalCutSetFn ?GRAPH)
?PATHCLASS)
(exists
(?NUMBER)
(forall
(?PATH)
(=>
(instance ?PATH ?PATHCLASS)
(pathLength ?PATH ?NUMBER)))))```

There don't exist the set of paths that partition graph into two separate graphs path1,the set of minimal paths that partition graph into two separate graphs path2 so that the length of path1 is number1 and the length of path2 is number2 and number1 is less than number2.
```(not
(exists
(?PATH1 ?PATH2)
(and
(instance
?PATH1
(CutSetFn ?GRAPH))
(instance
?PATH2
(MinimalCutSetFn ?GRAPH))
(pathLength ?PATH1 ?NUMBER1)
(pathLength ?PATH2 ?NUMBER2)
(lessThan ?NUMBER1 ?NUMBER2))))```