A note on the minimum cut cover of graphs

Authors:
Ho Tung-Yang;Hsu Lih-Hsing
Affiliations:
Department of Computer and Information Science, National Chiao-Tung University, Hsinchu, Taiwan 30050, R.O.C.;Department of Computer and Information Science, National Chiao-Tung University, Hsinchu, Taiwan 30050, R.O.C.
Venue:
Operations Research Letters
Year:
1994

Citing 3
Cited 0

Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Graph Theory With Applications

Graph Theory With Applications
Minimal cut cover of a graph with an application to the testing of electronic boards

Operations Research Letters

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Abstract

Loulou formulates the problem of minimizing the test time for printed circuit boards into that of minimizing the cardinality of cut cover for graphs. This note shows that the minimum cardinality of cut cover for a graph G is @?log"2 @g(G)@?. This result enables us to conclude that the problem of determining the minimum cardinality of cut cover is NP-hard. It is also known that every planar graph is 4-colorable. Thus, if the layouts of printed circuit board form a planar graph, the minimum time needed to test the circuits is at most 2.