MinimalCutSetFn - Sigma Knowledge base Browser

appearance as argument number 1

(instance MinimalCutSetFn UnaryFunction)	Merge.kif 6197-6197	Minimal cut set is an instance of unary function
(domain MinimalCutSetFn 1 Graph)	Merge.kif 6198-6198	The number 1 argument of minimal cut set is an instance of graph
(rangeSubclass MinimalCutSetFn GraphPath)	Merge.kif 6199-6199	The values returned by minimal cut set are subclasses of graph path
(relatedInternalConcept MinimalCutSetFn CutSetFn)	Merge.kif 6200-6200	Minimal cut set is internally related to cut set
(documentation MinimalCutSetFn EnglishLanguage "A UnaryFunction that assigns a Graph the Class of GraphPaths which comprise cutsets for the Graph and which have the least number of GraphArcs.")	Merge.kif 6202-6204	Minimal cut set is internally related to cut set

appearance as argument number 2

(termFormat EnglishLanguage MinimalCutSetFn "minimal cut set")	domainEnglishFormat.kif 37865-37865
(termFormat ChineseTraditionalLanguage MinimalCutSetFn "最小割集")	domainEnglishFormat.kif 37866-37866
(termFormat ChineseLanguage MinimalCutSetFn "最小割集")	domainEnglishFormat.kif 37867-37867
(format EnglishLanguage MinimalCutSetFn "the set of minimal paths that partition %1 into two separate graphs")	english_format.kif 779-779

antecedent

(=>
    (equal
        (MinimalCutSetFn ?GRAPH) ?PATHCLASS)
    (exists (?NUMBER)
        (forall (?PATH)
            (=>
                (instance ?PATH ?PATHCLASS)
                (pathLength ?PATH ?NUMBER)))))

Merge.kif 6210-6216

If equal the set of minimal paths that partition X into two separate graphs and Y, then there exists Z such that W W is an instance of Ythe length of W is Z

consequent

(=>
    (instance ?GRAPH Graph)
    (subclass
        (MinimalCutSetFn ?GRAPH)
        (CutSetFn ?GRAPH)))

Merge.kif 6206-6208

If X is an instance of graph, then the set of minimal paths that partition X into two separate graphs is a subclass of the set of paths that partition X into two separate graphs

statement

(not
    (exists (?PATH1 ?PATH2)
        (and
            (instance ?PATH1
                (CutSetFn ?GRAPH))
            (instance ?PATH2
                (MinimalCutSetFn ?GRAPH))
            (pathLength ?PATH1 ?NUMBER1)
            (pathLength ?PATH2 ?NUMBER2)
            (lessThan ?NUMBER1 ?NUMBER2))))

Merge.kif 6218-6225

There don't exist X, Y such that X is an instance of the set of paths that partition Z into two separate graphs, Y is an instance of the set of minimal paths that partition Z into two separate graphs, the length of X is W, the length of Y is V, and W is less than V

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