For a given edge (u, v) with endpoints u ∈ Vi and v ∈ Vi+1 we consider an adjacent double star with two centers at u and v, and sharing all the endpoints xj in the other graph parts, denoted as dstar(u, v); the weight of such a dstar(u, v) is 2wuv+∑j≠ij≠i+1(wuxj+wvxj) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqaIYaGmcqWG3bWDdaWgaaWcbaGaemyDauNaemODayhabeaakiabgUcaRmaaqadabaGaeiikaGIaem4DaC3aaSbaaSqaaiabdwha1jabdIha4naaBaaameaacqWGQbGAaeqaaaWcbeaakiabgUcaRiabdEha3naaBaaaleaacqWG2bGDcqWG4baEdaWgaaadbaGaemOAaOgabeaaaSqabaGccqGGPaqkaSqaauaabeqaceaaaeaacqWGQbGAcqGHGjsUcqWGPbqAaeaacqWGQbGAcqGHGjsUcqWGPbqAcqGHRaWkcqaIXaqmaaaabaaaniabggHiLdaaaa@4EE6@. Now consider a clique {u1 ∈ V1, ..., uN ∈ VN} of some value C*, and the sum of its double stars: