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Abstract: We continue the study of (tw, ω)‐bounded graph classes, that is, hereditary graph classes in which large treewidth is witnessed by the presence of a large clique, and the relation of this property to boundedness of the tree‐independence number, a graph parameter introduced independently by Yolov in 2018 and by Dallard, Milanič, and Štorgel in 2024. Dallard et al. showed that bounded tree‐independence number is sufficient for (tw, ω)‐boundedness, and conjectured that the converse holds. While this conjecture has been recently disproved, it is still interesting to determine classes where the conjecture holds; for example, the conjecture is still open for graph classes excluding an induced star, as well as for finitely many forbidden induced subgraphs. In this paper, we identify further families of graph classes where (tw, ω)‐boundedness is equivalent to bounded tree‐independence number. We settle a number of cases of finitely many forbidden induced subgraphs, obtain several equivalent characterizations of (tw, ω)-boundedness in subclasses of the class of complements of line graphs, and give a short proof of a recent result of Ahn, Gollin, Huynh, and Kwon [SODA 2025] establishing bounded tree-independence number for graphs excluding a fixed induced star and a fixed number of independent cycles.
Keywords: clique number, hereditary graph class, line graph, tree‐independence number, treewidth
Published in RUP: 09.04.2026; Views: 85; Downloads: 2
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Abstract: Faced with the enormity of Hexagrammum Mysticum, trying to understand it and wishing to discover in it something genuinely new, I decided to first try my hand at something smaller and easier to handle, to get some practice. To this end I have chosen the Pappus layout of two lines with three points on each, a degenerate variation of the Pascal’s sextet of coconic points which is the construction base of Hexagramum Mysticum. I permuted the points on one of the lines, and generated the six Pappus three-point lines corresponding to the permuted hexagons. Six three-point lines was too little material even for a Hexagrammum Brevis, so I adopted into the configuration the nine lines connecting pairs of points on the opposite lines of a Pappus layout, and for good measure added the two points of concurrence of two tercets of Pappus lines. The resulting Frankenstein Creature configuration, sewed together from three so different parts, surprisingly turned out to be the highly symmetric Adler configuration, of type (20, 15). And this was only the warm-up. After some slightly weird configuration mining I dug up thirty-three configurations of type (21), the inward Pappus configurations (as I named them), that are partitioned into four classes of isomorphic combinatorial configurations. Besides that I found also a cross-eyed cousin to the Desargues configuration, of type (10), and then, using a special geometric realization of this configuration, composed a configuration of type (28, 21).
Keywords: Pappus line, Pappus layout, configuration, incidence, collinearity, concurrence
Published in RUP: 03.03.2026; Views: 219; Downloads: 5
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Abstract: Aureobasidium melanogenum is a black yeast-like fungus that occurs frequently both in nature and in domestic environments. It is becoming increasingly important as an opportunistic pathogen. Nevertheless, its effect on human cells has not yet been studied. In this study, we investigated the effect of A. melanogenum cells and extracellular vesicles (EVs) on human cell lines A549 (human lung cells), HDFa (human dermal fibroblasts), and SH-SY5Y (human neuroblastoma cells). Scanning electron microscopy (SEM) showed no direct interaction between A. melanogenum cells and human cell lines, but there were some changes in HDFa cells. As a possible cause for this change, we tested the cytotoxic effect of EVs from A. melanogenum on the same cell lines. We isolated EVs from the fungus and prepared three different pools: a non-melanin pool (containing mainly EVs), a melanin pool (containing mainly melanin nanoparticles), and a total pool (containing both EVs and melanin nanoparticles). All three pools were characterized and then added to human cell lines to test their cytotoxicity. Unlike in some other fungal opportunistic pathogens, no effects of fungal EVs on human cell viability were observed. Therefore, the opportunistic potential of A. melanogenum remains only partially understood.
Keywords: extracellular vesicles, Aureobasidium melanogenum, pathogenesis, melanin, human cell line
Published in RUP: 07.08.2025; Views: 725; Downloads: 5
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Keywords: point-line configuration, conic section, point-ellipse configuration, point-conic configuration, Levi graph, Carnot's theorem
Published in RUP: 18.10.2021; Views: 4539; Downloads: 27
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Keywords: wood surface smoothness, triangulation scanner, surface defects, in-line
Published in RUP: 17.06.2020; Views: 4332; Downloads: 52
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