The conclusion of the classical ham sandwich theorem of Banach and Steinhaus may be strengthened: there always exists a common bisecting hyperplane that touches each of the sets, that is, intersects the closure of each set. Hence, if the knife is smeared with mayonnaise, a cut can always be made so that it will not only simultaneously bisect each of the ingredients, but it will also spread mayo...

In this paper, we mainly deal with sequences of bounded linear operators on Hilbert space. The main result is the so-called squeeze theorem (or sandwich rule) for convergent self-adjoint operators. We show that remains valid all three topologies B(H). Some interesting consequences are given.

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We show that under suitable non-degeneracy conditions, m points and n 2–dimensional algebraic surfaces in R satisfying certain “pseudoflat” requirements can have at most O ( mn + m + n ) incidences, provided that m ≤ n2− for any > 0 (where the implicit constant in the above bound depends on ), or m ≥ n. As a special case, we obtain the Szemerédi-Trotter theorem for 2–planes in R, again provided...

The conclusion of the classical ham sandwich theorem for bounded Borel sets may be strengthened, without additional hypotheses – there always exists a common bisecting hyperplane that touches each of the sets, that is, that intersects the closure of each set. In the discrete setting, where the sets are finite (and the measures are counting measures), there always exists a bisecting hyperplane t...

A certain class of integral operators Jβ,γ(f), γ, β ∈ C, β ∈ C\{0} and R(γ − β) > 1/2, of meromorphic functions in the punctured open unit disk is introduced. The main object of this paper is to investigate some subordination and superordination preserving properties of these integral operators with the sandwich type theorem.

The independence number, coloring number and related parameters are investigated in the setting of oriented hypergraphs using spectrum normalized Laplace operator. For both an inertia--like bound a ratio--like shown. A Sandwich Theorem involving clique vector chromatic is proved, as well lower for terms smallest largest eigenvalue Laplacian. In addition, spectral partition numbers studied relat...

X iv :1 70 4. 01 92 2v 1 [ m at h. C O ] 6 A pr 2 01 7 Sandwiches Missing Two Ingredients of Order Four José D. Alvarado Simone Dantas Dieter Rautenbach 1 Instituto de Matemática e Estat́ıstica, Universidade Federal Fluminense, Niterói, Brazil [email protected], [email protected] 2 Institute of Optimization and Operations Research, Ulm University, Ulm, Germany dieter.rautenbach@uni-ul...

In a recent paper, we introduced the simultaneous representation problem (defined for any graph class C) and studied the problem for chordal, comparability and permutation graphs. For interval graphs, the problem is defined as follows. Two interval graphs G1 and G2, sharing some vertices I (and the corresponding induced edges), are said to be “simultaneous interval graphs” if there exist interv...