High grade serous ovarian cancer (HGSOC) is the most common and aggressive ovarian cancer subtype with the worst clinical outcome due to intrinsic or acquired drug resistance. Standard treatment involves platinum compounds. Cancer development and chemoresistance is often associated with an increase in histone deacetylase (HDAC) activity. The purpose of this study was to examine the potential of HDAC inhibitors (HDACi) to increase platinum potency in HGSOC. Four HGSOC cell lines with different cisplatin sensitivity were treated with combinations of cisplatin and entinostat (class I HDACi), panobinostat (pan-HDACi), or nexturastat A (class IIb HDACi), respectively. Inhibition of class I HDACs by entinostat turned out superior in increasing cisplatin potency than pan-HDAC inhibition in cell viability assays (MTT), apoptosis induction (subG1), and caspase 3/7 activation. Entinostat was synergistic with cisplatin in all cell lines in MTT and caspase activation assays. MTT assays gave combination indices (CI values) < 0.9 indicating synergism. The effect of HDAC inhibitors could be attributed to the upregulation of pro-apoptotic genes (CDNK1A, APAF1, PUMA, BAK1) and downregulation of survivin. In conclusion, the combination of entinostat and cisplatin is synergistic in HGSOC and could be an effective strategy for the treatment of aggressive ovarian cancer.

Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-width under various unary and binary graph transformations. For considered transformations, we provide upper and lower bounds for the tree-width and path-width of the resulting graph in terms of those of the initial graphs or argue why such bounds are impossible to specify. Among the studied unary transformations are vertex addition, vertex deletion, edge addition, edge deletion, subgraphs, vertex identification, edge contraction, edge subdivision, minors, powers of graphs, line graphs, edge complements, local complements, Seidel switching, and Seidel complementation. Among the studied binary transformations, we consider the disjoint union, join, union, substitution, graph product, 1-sum, and corona of two graphs.

Frei et al. (J. Comput. Syst. Sci. 123, 103–121, 2022) show that the stability, vertex stability, and unfrozenness problems with respect to certain graph parameters are complete for $$\varvec{\Theta _{2}^{\textrm{P}}}$$Θ 2 P , the class of problems solvable in polynomial time by parallel access to an NP oracle. They studied the common graph parameters $$\varvec{\alpha }$$α (the independence number), $$\varvec{\beta }$$β (the vertex cover number), $$\varvec{\omega }$$ω (the clique number), and $$\varvec{\chi }$$χ (the chromatic number). We complement their approach by providing polynomial-time algorithms solving these problems for special graph classes, namely for graphs with bounded tree-width or bounded clique-width. In order to improve these general time bounds even further, we then focus on trees, forests, bipartite graphs, and co-graphs.

Cake-cutting is a playful name for the fair division of a heterogeneous, divisible good among agents, a well-studied problem at the intersection of mathematics, economics, and artificial intelligence. The cake-cutting literature is rich and edifying. However, different model assumptions are made in its many papers, in particular regarding the set of allowed pieces of cake that are to be distributed among the agents and regarding the agents' valuation functions by which they measure these pieces. We survey the commonly used definitions in the cake-cutting literature, highlight their strengths and weaknesses, and make some recommendations on what definitions could be most reasonably used when looking through the lens of measure theory.