Seven-pinhole emission tomography has been studied under conditions that simulate clinical myocardial imaging with thallium-201, and is compared with planar imaging with a heart phantom. The seven-pinhole technique produces reconstructed images that offer a tomographic presentation of the object but do not quantitatively represent true cross sections of the object's activity distribution. Tomog...

Recently, some advanced algorithms for straight line drawings of planar graphs have been introduced. However, these algorithms produce drawings with many small angles. Their drawings are not aesthetically nice. Our goal is to resolve these problems by a beautifier. We consider the angles of planar straight line drawings. In a first phase we compute maximal angles by repeatedly solving a linear ...

The moving sofa problem, posed by L. Moser in 1966, asks for the planar shape of maximal area that can move around a right-angled corner in a hallway of unit width. It is known that a maximal area shape exists, and that its area is at least 2.2195 . . .—the area of an explicit construction found by Gerver in 1992—and at most 2 √ 2 ≈ 2.82, with the lower bound being conjectured as the true value...

If G is a 4-connected maximal planar graph, then G is hamiltonian (by a theorem of Whitney), implying that its dual graph G∗ is a cyclically 4-edge connected 3regular planar graph admitting a partition of the vertex set into two parts, each inducing a tree in G∗, a so-called tree-partition. It is a natural question whether each cyclically 4-edge connected 3-regular graph admits such a tree-part...

The weighted maximal planar graph (WMPG) problem seeks to find a subgraph from a given weighted complete graph such that the subgraph is planar—it can be embedded on the plane without any arcs intersecting. The subgraph is maximal—no additional arc can be added to the subgraph without destroying its planarity and it also has the maximal sum of arc weights. In this paper, the main objective is t...

An induced matching M of a graph G is a set of pairwise non-adjacent edges such that their end-vertices induce a 1-regular subgraph. An induced matching M is maximal if no other induced matching contains M . The MINIMUM MAXIMAL INDUCED MATCHING problem asks for a minimum maximal induced matching in a given graph. The problem is known to be NP-complete. Here we show that, if P 6= NP, for any ε >...

Given P and P ′, equally sized planar point sets in general position, we call a bijection from P to P ′ crossing-preserving if crossings of connecting segments in P are preserved in P ′ (extra crossings may occur in P ′). If such a mapping exists, we say that P ′ crossing-dominates P , and if such a mapping exists in both directions, P and P ′ are called crossing-equivalent. The relation is tra...

Let On be the set of all maximal outer-planar graphs order n. ar(On,F) denote maximum positive integer k such that there is a k-edge-coloring graph T in family which has no rainbow subgraph F. Denote by Mk matching size k. In this paper, we prove ar(On,Mk)≤n+4k−9 for n≥3k−3, expressively improves existing upper bound ar(On,Mk). We also ar(On,M5)=n+4 n≥15.