In the seminal work [8] L. Lovász introduced the concept of an orthonormal representation of a graph, and also a related value, now popularly known as the Lovász number of the graph. One of the remarkable properties of the Lovász number is that it lies sandwiched between the stability number and the complementer chromatic number. This fact is called the sandwich theorem. In this paper, using ne...

The traditional proofisa clev eruseoftheBorsuk-Ulamtheorem;see[1,p.120] . As Munkresremarks[5,p.405] ,theham sandwic h theoremisnotelemen tary ,evenindimension2,whereitisknown asthebabyham sandwichtheorem. But isitreally sohard? Consider thefollo wing:\aplanethroughthecentresofgravit y ofeach ofthebodieswill dothetric k" [3,p.57].Unfortunately ,thiseductiv eargumentjustdoesn’t work:a plane thro...

In this short note we utilize the Borsuk-Ulam Anitpodal Theorem to present a simple proof of the following generalization of the “Ham Sandwich Theorem”: Let A1, . . . , Am ⊆ R be subsets with finite Lebesgue measure. Then, for any sequence f0, . . . , fm of R-linearly independent polynomials in the polynomial ring R[X1, . . . , Xn] there are real numbers λ0, . . . , λm, not all zero, such that ...

MOTIVATION Giving a meaningful representation of a pedigree is not obvious when it includes consanguinity loops, individuals with multiple mates or several related families. RESULTS We show that finding a perfectly meaningful representation of a pedigree is equivalent to the interval graph sandwich problem and we propose an algorithm for drawing pedigrees.

In a Z-core sandwich panel, the shear stiffness of the sandwich panel in the weak direction which is perpendicular to the placement of the Z-cores is much smaller than the bending stiffness because the hollow section between the two facing plates cannot sustain shear action. Because of this fact, the shear deformation of a Z-core sandwich panel under bending in the weak direction cannot be igno...

In this study, a sandwich beam with periodic multiple dissipative resonators in the sandwich core material is investigated for broadband wave mitigation and/or absorption. An analytical approach based on the transfer matrix method and Bloch theorem is developed for both infinite and finite sandwich structures. Wave attenuation constants are theoretically obtained to examine the effects of vario...