Automotive manufacturers are under stressful timelines as they shift their focus from internal combustion engines (ICE) to electric (EV) and hybrid-electric vehicles (HEV). The demand for this rapid change is crucial meet a growing consumer market. New manufacturing challenges coupled with can lead substantial safety risks consumers well financial liability automakers, especially when recalls h...

We announce results about flat (linkless) embeddings of graphs in 3space. A piecewise-linear embedding of a graph in 3-space is called flat if every circuit of the graph bounds a disk disjoint from the rest of the graph. We have shown: (i) An embedding is flat if and only if the fundamental group of the complement in 3-space of the embedding of every subgraph is free. (ii) If two flat embedding...

A 2-page book embedding of a graph is to place the vertices linearly on a spine (a line segment) and the edges on the two pages (two half planes sharing the spine) so that each edge is embedded in one of the pages without edge crossings. Testing whether a given graph admits a 2-page book embedding is known to be NP-complete. In this paper, we study the problem of testing whether a given graph a...