简介:AsubsetofSofthevertexsetofagraphGiscalledacyclicifthesubgraphitinducesinGcontainsnocycles.SiscalledanacyclicdominatingsetofGifitisbothacyclicanddominating.Theminimumcardinalityofanacyclicdominatingset,denotedbyγα(G),iscalledtheacyclicdominationnumberofG.S.M.Hedetniemietal.on2000introducedtheconceptofacyclicdominationandposedthefollowingopenproblem:Isγα(G)≤δ(G)foranygraphwhosediameteristwo?Inthispaper,wegiveacounterexamplewhichdisprovestheproblem.
简介:Inrecentyears,therearemanycrimesrelateddrugfraudoccuringinChinaandmanyexpertsthinkthatthemaincauseisthatChinaFoodandDrugAdministration(CFDA)adoptsannouncedinspection(AI).Inordertocircumventthisdifficulty,CFDAhasexploitedunannouncedinspection(UI)since2014.Inthispaper,theauthorsstudytheproblemofwhichoneperformsbetter,AIorUI.Specifically,theauthorsconsiderasupervisor,whichdecidestheinspectionapproach,inspectionstrengthandpunishmenttoforcethefirmtoputself-inspectionefforttomeettherequirementsofGoodManufacturingPractice,andafirm,whichproducesadruganddecidesitsself-inspectioneffort.Theauthorsusegametheorytomodelthisproblem,characterizetheequilibriumpoliciesunderAI,andcomparetheeffectsofthetwoapproachesonpreventingdrugfraudundercompleteandincompleteinformation.Theresultsshowthatunderthecompleteinformation,UIperformsbetterifthefirm'stechnicallevelandtheinspectioncostarelowandAIperformsbetterotherwise.Whenthesupervisordoesn'tknowthefirm'stechnicallevel,ifthelowtechnicallevelishigh,AIperformsbetter.Otherwise,UIperformsbetteriftheinspectioncostislowandAIperformsbetteriftheinspectioncostishigh.