Highly edge-connected regular graphs without large factorizable subgraphs

We construct highly edge-connected $r$-regular graphs of even order which do not contain $r?2$ pairwise disjoint perfect matchings. When $r$ is a multiple of 4, the result solves a problem of Thomassen [4].     

On the use of AES data analysis to determine local enrichments of conversion coating elements at intermetallic particles on rolled Al

In this paper, the behaviour of the industrial applied Ti/Zr conversion coating (CC) pretreatment on rolled automotive aluminium samples (AA5182) is analysed. Due to its nanometre lateral and depth resolution, Auger electron spectroscopy (AES) is used to analyse the CC distribution at surface cathodic intermetallic particles. As a result of its high surface sensitivity, the AES technique is very susceptible to differences in the top contamination layer thickness. It is demonstrated that AES point measurements performed on aluminium model samples coated with 1.5 and 3 nm of Ti (oxide) layer cannot differentiate the two-layer thicknesses if a difference in the top contamination thickness is not taken into account. A data analysis methodology is introduced, based on the ratio of normalized peak areas (enrichment ratios), to eliminate the effect of the contamination layer thickness. The experimental validation of the methodology is performed on the model samples, demonstrating errors of 2% on the enrichment ratios on similar samples with different contamination layer thicknesses, while the conventional spectra quantification results in errors of 49%. The methodology is also theoretically substantiated within certain constraints. By the use of the AES methodology, an enriched Ti and Zr deposition is confirmed at the cathodic intermetallic particles at the surface of the industrial no-rinse CC sprayed automotive aluminium sheet samples.     

Oleogels—Their Applicability and Methods of Characterization

Oleogels or, more precisely, non-triglyceride structured lipid phases have been researched excessively in the last decade. Yet, no comprehensive knowledge base has emerged, allowing technology elevation from the laboratory bench into the industrial food application. That is partly due to insufficient characterization of the structuring systems studied. Examining a single composition decided upon by arbitrary methods does not stimulate progress in the research and technology area. A framework that gives much better guidance to product applications can easily be derived. For example, the incremental structure contribution concept is advocated as a parameter to compare the potency of structuring systems. These can straightforwardly be determined by combining solubility data and structural measurements in the recommended manner. The current method to determine the oil-binding capacity suffers from reproducibility and relevance. A newly developed method is suggested to overcome these shortcomings. The recommended new characterization of oleogels should contribute to a more comprehensive knowledge base necessary for product innovations.     

Cyanide Binding to [FeFe]-Hydrogenase Stabilizes the Alternative Configuration of the Proton Transfer Pathway

Hydrogenases are H₂ converting enzymes that harbor catalytic cofactors in which iron (Fe) ions are coordinated by biologically unusual carbon monoxide (CO) and cyanide (CN⁻) ligands. Extrinsic CO and CN⁻, however, inhibit hydrogenases. The mechanism by which CN⁻ binds to [FeFe]-hydrogenases is not known. Here, we obtained crystal structures of the CN⁻-treated [FeFe]-hydrogenase CpI from Clostridium pasteurianum. The high resolution of 1.39 Å allowed us to distinguish intrinsic CN⁻ and CO ligands and to show that extrinsic CN⁻ binds to the open coordination site of the cofactor where CO is known to bind. In contrast to other inhibitors, CN⁻ treated crystals show conformational changes of conserved residues within the proton transfer pathway which could allow a direct proton transfer between E279 and S319. This configuration has been proposed to be vital for efficient proton transfer, but has never been observed structurally.     

Folding of the Tau Protein on Microtubules

Microtubules are regulated by microtubule‐associated proteins. However, little is known about the structure of microtubule‐associated proteins in complex with microtubules. Herein we show that the microtubule‐associated protein Tau, which is intrinsically disordered in solution, locally folds into a stable structure upon binding to microtubules. While Tau is highly flexible in solution and adopts a β‐sheet structure in amyloid fibrils, in complex with microtubules the conserved hexapeptides at the beginning of the Tau repeats two and three convert into a hairpin conformation. Thus, binding to microtubules stabilizes a unique conformation in Tau.     

Nowhere‐Zero 5‐Flows On Cubic Graphs with Oddness 4

Tutte's 5‐flow conjecture from 1954 states that every bridgeless graph has a nowhere‐zero 5‐flow. It suffices to prove the conjecture for cyclically 6‐edge‐connected cubic graphs. We prove that every cyclically 6‐edge‐connected cubic graph with oddness at most 4 has a nowhere‐zero 5‐flow. This implies that every minimum counterexample to the 5‐flow conjecture has oddness at least 6.     

Petersen Cores and the Oddness of Cubic Graphs

Let G be a bridgeless cubic graph. Consider a list of k 1‐factors of G. Let be the set of edges contained in precisely i members of the k 1‐factors. Let be the smallest over all lists of k 1‐factors of G. We study lists by three 1‐factors, and call with a ‐core of G. If G is not 3‐edge‐colorable, then . In Steffen (J Graph Theory 78 (2015), 195–206) it is shown that if , then is an upper bound for the girth of G. We show that bounds the oddness of G as well. We prove that . If , then every ‐core has a very specific structure. We call these cores Petersen cores. We show that for any given oddness there is a cyclically 4‐edge‐connected cubic graph G with . On the other hand, the difference between and can be arbitrarily big. This is true even if we additionally fix the oddness. Furthermore, for every integer , there exists a bridgeless cubic graph G such that .