We give eecient algorithms to compute an optimal bipartition of a set of points or a set of simple polygons in the plane. In particular, we give an O(n 2) algorithm for partitioning a set of n points into two subsets in order to minimize the sum of the perimeters of the convex hulls. We also examine the problems of minimizing the maximum of the perimeters, or the sum/maximum of the areas, for t...

The trees, respectively unicyclic graphs, on n vertices with the smallest Laplacian permanent are studied. In this paper, by edge-grafting transformations, the n-vertex trees of given bipartition having the second and third smallest Laplacian permanent are identified. Similarly, the n-vertex bipartite unicyclic graphs of given bipartition having the first, second and third smallest Laplacian pe...

The trees, respectively unicyclic graphs, on n vertices with the smallest Laplacian permanent are studied. In this paper, by edge-grafting transformations, the n-vertex trees of given bipartition having the second and third smallest Laplacian permanent are identified. Similarly, the n-vertex bipartite unicyclic graphs of given bipartition having the first, second and third smallest Laplacian pe...

In this paper, we study the parameterized complexity of the problems of partitioning the vertex set of a graph into two parts VA and VB such that VA induces a graph with degree at most a (resp., an a-regular graph) and VB induces a graph with degree at most b (resp., a b-regular graph). These two problems are called Upper-Degree-Bounded Bipartition and Regular Bipartition respectively. First, w...

Let G be a bipartite graph, and let H be a bipartite graph with a fixed bipartition (BH ,WH). We consider three different, natural ways of forbidding H as an induced subgraph in G. First, G is H-free if it does not contain H as an induced subgraph. Second, G is strongly H-free if G is H-free or else has no bipartition (BG,WG) with BH ⊆ BG and WH ⊆ WG. Third, G is weakly H-free if G is H-free or...

OBJECTIVE Sleeve gastrectomy is the fastest growing surgical procedure to treat obesity in the world but it may cause or worsen gastroesophageal reflux disease. This article originally aimed to describe the addition of anti-reflux procedures (removal of periesophageal fats pads, hiatoplasty, a small plication and fixation of the gastric remnant in position) to the usual sleeve gastrectomy and t...

We studied the importance of proper model assumption in the context of Bayesian phylogenetics by examining >5,000 Bayesian analyses and six nested models of nucleotide substitution. Model misspecification can strongly bias bipartition posterior probability estimates. These biases were most pronounced when rate heterogeneity was ignored. The type of bias seen at a particular bipartition appeared...