Titlebook: ;

BADGE

The Complexity of?Recognizing Geometric Hypergraphslfspaces in .. We study the families of translates of balls and ellipsoids in ., as well as of other convex sets, and show that their . problems are also .-complete. This means that these recognition problems are equivalent to deciding whether a multivariate system of polynomial equations with integer coefficients has a real solution.

ALE

anthropologist

Lucubrate

割公牛膨脹

https://doi.org/10.1007/978-3-031-48565-7. We disprove a conjecture of Gethner that 2-blowups of planar graphs are biplanar: iterated Kleetopes are counterexamples. Additionally, we construct biplanar drawings of 2-blowups of planar graphs whose duals have two-path induced path partitions, and drawings with split thickness two of 2-blowups

Tracheotomy

進(jìn)步

https://doi.org/10.1007/978-3-031-18432-1r of edges can only cross at a right angle, has at most . edges for .. This improves upon the previous upper bound of 74.2.; this is the first improvement in more than 12 years. A crucial ingredient of the proof is an upper bound on the size of plane multigraphs with polyline edges in which the firs

肉身

Midwifery, Childbirth and the Media intersects in at most . points. We introduce the class of .-string graphs as a further restriction of .-string graphs by requiring that every two curves intersect in either zero or precisely . points. We study the hierarchy of these graphs, showing that for any ., .-string graphs are a subclass of

Limerick

Midwives, Research and Childbirtharcs and multiple edges passing through the same point are counted as a single crossing. Interpreting each crossing as a cross-cap induces an embedding into a non-orientable surface. In 2007, Mohar showed that the degenerate crossing number of a graph is at most its non-orientable genus and he conje

Cholecystokinin

Midwives, Research and Childbirth satisfy some property that is useful for graph visualization. We propose investigating a property where each edge is not crossed in at least one drawing in the collection. We call such collection .. This property is motivated by a quintessential problem of the crossing number, where one asks for a