Per- and polyfluoroalkyl substances (PFAS), a highly persistent and potentially toxic class of chemicals, are added to cosmetics to increase their durability and water resistance. To assess this potential health and environmental risk, 231 cosmetic products purchased in the U.S. and Canada were screened for total fluorine using particle-induced gamma-ray emission spectroscopy. Of the eight categories tested, foundations, mascaras, and lip products had the highest proportion of products with high total fluorine ≥0.384 μg F/cm2. Twenty-nine products including 20 with high total fluorine concentrations were analyzed using targeted LC-MS/MS and GC-MS. PFAS concentrations ranged from 22–10,500 ng/g product weight, with an average and a median of 264 and 1050 ng/g product weights, respectively. Here, 6:2 and 8:2 fluorotelomer compounds, including alcohols, methacrylates, and phosphate esters, were most commonly detected. These compounds are precursors to PFCAs that are known to be harmful. The ingredient lists of most products tested did not disclose the presence of fluorinated compounds exposing a gap in U.S. and Canadian labeling laws. The manufacture, use, and disposal of cosmetics containing PFAS are all potential opportunities for health and ecosystem harm. Given their direct exposure routes into people, better regulation is needed to limit the widespread use of PFAS in cosmetics.

Occupational exposure to aqueous film-forming foams (AFFF) can lead to elevated concentrations of per-and polyfluorinated alkyl substances (PFAS) in firefighter blood sera. AFFF are also one exposure source of PFAS in the general population because of their environmental persistence and solubility in groundwater. Because of the documented adverse health effects of PFAS, the primary concern to date in the fire services has centered on repeated use and exposure to AFFF. In this work, an additional PFAS exposure source for firefighters is presented: PFAS that are shed from their protective clothing. Textiles used as firefighter turnout gear were found to have high levels of total fluorine (up to 2%), and individual PFAS were identified and measured on new and used firefighting turnout gear. Used gear showed lower levels of PFAS as well as an increased migration into untreated material. A dust measurement from a textile storage area also suggests direct loss of PFAS from the fluoropolymers in the textiles. Because PFAS that are shed from the textiles used in turnout gear are more mobile, they represent another viable exposure source for firefighters that warrants further study.

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Per-and polyfluoroalkyl substances (PFASs) represent a class of more than 4000 compounds. Their large number and structural diversity pose a considerable challenge to analytical chemists. Measurement of total fluorine in environmental samples and consumer products is therefore critical for rapidly screening for PFASs and for assessing the fraction of unexplained fluorine(i.e., fluorine mass balance). Here we compare three emerging analytical techniques for total fluorine determination: combustion ion chromatography (CIC), particle-induced γ-ray emission spectroscopy (PIGE), and instrumental neutron activation analysis (INAA). Application of each method to a certified reference material (CRM), spiked filters, and representative food packaging samples revealed good accuracy and precision. INAA and PIGE had the advantage of being nondestructive, while CIC displayed the lowest detection limits. Inconsistencies between the methods arose due to the high aluminum content in the CRM, which precluded its analysis by INAA, and sample heterogeneity (i.e., coating on the surface of the material), which resulted in higher values from the surface measurement technique PIGE compared to the values from the bulk volume techniques INAA and CIC. Comparing CIC-based extractable organic fluorine to target PFAS measurements of food packaging samples by liquid chromatography− tandem mass spectrometry revealed large amounts of unidentified organic fluorine not captured by compound-specific analysis.

In 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with maximum degree ∆ ≥ 8 is at most 3 2 ∆ + 1. We show that it is at most 3 2 ∆ (1 + o(1)).

Let p and q be positive integers with p/q ≥ 2. The "reconfiguration problem" for circular colourings asks, given two (p, q)-colourings f and g of a graph G, is it possible to transform f into g by changing the colour of one vertex at a time such that every intermediate mapping is a (p, q)-colouring? We show that this problem can be solved in polynomial time for 2 ≤ p/q < 4 and that it is PSPACE-complete for p/q ≥ 4. This generalizes a known dichotomy theorem for reconfiguring classical graph colourings. As an application of the reconfiguration algorithm, we show that graphs with fewer than (k − 1)!/2 cycles of length divisible by k are k-colourable.

Let G be the family of ®nite collections S where S is a collection of bounded, arcwise connected sets in R 2 which for any SY T e S where S T H h, it holds that S T is arcwise connected. We investigate the problem of bounding the chromatic number of the intersection graph G of a collection S e G.Assuming G is triangle-free, suppose there exists a closed Jordan curve C r R 2 such that C intersects all sets of S and for all S e S, the following holds:Here intC and extC denote the regions in the interior, resp. exterior, of C. Such being the case, we shall show that wS is bounded by a constant independent of S.

We prove that a cubic 2-connected graph which has a 2-factor containing exactly 4 odd cycles has a cycle double cover.