Every Graph Is an Integral Distance Graph in the Plane

We prove that every finite simple graph can be drawn in the plane so that any two vertices have an integral distance if and only if they are adjacent. The proof is constructive.     

Chromatic numbers of quadrangulations on closed surfaces

It has been shown that every quadrangulation on any nonspherical orientable closed surface with a sufficiently large representativity has chromatic number at most 3. In this paper, we show that a quadrangulation G on a nonorientable closed surface N_k has chromatic number at least 4 if G has a cycle of odd length which cuts open N_k into an orientable surface. Moreover, we characterize the quadrangulations on the torus and the Klein bottle with chromatic number exactly 3. By our characterization, we prove that every quadrangulation on the torus with representativity at least 9 has chromatic number at most 3, and that a quadrangulation on the Klein bottle with representativity at least 7 has chromatic number at most 3 if a cycle cutting open the Klein bottle into an annulus has even length. As an application of our theory, we prove that every nonorientable closed surface N_k admits an eulerian triangulation with chromatic number at least 5 which has arbitrarily large representativity. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 100–114, 2001     

Statistics of Gaussian Speckles with Enhanced Fluctuations

Some first-order statistics of speckle fields obeying the complex Gaussian probability density are investigated with the special emphasis on a possibility for the speckle contrast to exceed unity. It is shown that such enhanced fluctuations of speckle fields are generated when the probability density of the complex amplitude is non-circular with the vanishing mean. This means that Gaussian speckles having the contrast of unity are not necessarily fully developed speckles. Some practical situations producing such enhanced fluctuations in speckle fields are discussed.     

Measurement of optical constants for dense media by low-coherence dynamic light scattering

We perform the optical constants measurements for different absorption dense media by low-coherence dynamic light scattering (DLS) technique. The estimated particle size is used to calculate the scattering coefficient of particles suspended in dense media. The path-length resolved intensity distributions of light backscattered from the absorbing dense media are investigated experimentally by virtue of path-length resolved performance in low-coherence DLS measurements. The absorption coefficient can be obtained by applying the measured path-length resolved intensity distributions to the modified Lambert-Beer law. As a result, we proposed a new low-coherence DLS technique in simultaneous measurement of the scattering and absorption coefficients of absorbing dense media.     

The Diameters of Some Transition Graphs Constructed from Hamilton Cycles

 A complete undirected graph of order n has Hamilton cycles. We consider the diameter of a transition graph whose vertices correspond to those Hamilton cycles and any of two vertices are adjacent if and only if the corresponding Hamilton cycles can be transformed each other by exchanging two edges. Moreover, we consider several transition graphs related to it. Received: November 4, 1999 Final version received: August 28, 2000     

Enantioselective catalysis of Claisen rearrangement by DABNTf-Pd(II) complex

Two types of palladium complexes, cationic and neutral (R)-DABNTf-Pd(CH₃CN)₂ were examined as chiral catalysts for enantioselective Claisen rearrangement. DABNTf-Pd(CH₃CN)₂ complex gave high enantio- and anti-diastereoselectivity, and good yield. This Claisen rearrangement should proceed via six-membered boat transition state through bi-dentate coordination to the Pd catalyst.