There are 526,915,620 nonisomorphic one-factorizations of K12

We enumerate the nonisomorphic and the distinct one-factorizations of K₁₂. We also describe the algorithm used to obtain the result, and the methods we used to verify these numbers. © 1994 John Wiley & Sons, Inc.     

Kinetics studies of rapid strain-promoted [3 + 2]-cycloadditions of nitrones with biaryl-aza-cyclooctynone

Strain-promoted cycloadditions of cyclic nitrones with biaryl-aza-cyclooctynone (BARAC) proceed with rate constants up to 47.3 M(-1) s(-1), this corresponds to a 47-fold rate enhancement relative to reaction of BARAC with benzyl azide and a 14-fold enhancement over previously reported strain promoted alkyne-nitrone cycloadditions (SPANC). Studies of the SPANC reaction using the linear free energy relationship defined by the Hammett equation demonstrated that the cycloaddition reaction has a rho value of 0.25 ± 0.04, indicating that reaction is not sensitive to substituents and thus should have broad applicability.     

Simultaneous brightness enhancement and wavelength conversion to the eye‐safe region in a high‐power diamond Raman laser

Brightness enhancement in an external cavity diamond Raman laser designed for high power conversion of a neodymium (1064 nm) laser to the eye‐safe spectral region is reported. Using a multimode input beam pulsed at 36 kHz pulse repetition frequency, 16.2 W with 40% overall conversion efficiency was obtained at the second Stokes wavelength of 1485 nm. The output beam had a quality factor of which is a factor of 2.7 times lower than that of the input beam, resulting in a higher overall brightness. The output power, brightness, and brightness enhancement obtained represent significant advances in performance for Raman lasers as well as other competing kHz‐pulsed eye‐safe technologies.     

Graphs with the n‐e.c. adjacency property constructed from resolvable designs

Only recently have techniques been introduced that apply design theory to construct graphs with the n‐e.c. adjacency property. We supply a new random construction for generating infinite families of finite regular n‐e.c. graphs derived from certain resolvable Steiner 2‐designs. We supply an extension of our construction to the infinite case, and thereby give a new representation of the infinite random graph. We describe a family of deterministic graphs in infinite affine planes which satisfy the 3‐e.c. property. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 294–306, 2009     

Linear Programming on Microcomputers

The paper considers the problems involved in implementing linear programming software on microcomputers and the user requirements for packages on such machines.     

The asymptotic number of claw-free cubic graphs

Let H_n be the number of claw-free cubic graphs on 2n labeled nodes. In an earlier paper we characterized claw-free cubic graphs and derived a recurrence relation for H_n. Here we determine the asymptotic behavior of this sequence: