简介:GivenacompletegraphwithvertexsetXandsubsetsX1,X2,...,Xn,theproblemoffindingasubgraphGwithminimumnumberofedgessuchthatforeveryi=1,2,...,n,GcontainsaspanningtreeonXi,arisesinthedesignofvaccumsystems.Ingeneral,thisproblemisNP-completeanditisprovedthatforn=2and3thisproblemispolynomial-timesolvable.Inthispaper,weprovethatforn=4,theproblemisalsopolynomial-tlmesolvableandgiveamethodtoconstructthecorrespondinggraph.