We propose Inflate-Paste – a new technique for generating orthogonal polygons with a given number of vertices from a unit square based on gluing rectangles. It is dual to Inflate-Cut – a technique we introduced in [12] that works by cutting rectangles.

For a positive integer d, the d-CUT is problem of deciding if an undirected graph $$G=(V,E)$$ has nontrivial bipartition (A, B) V such that every vertex in A (resp. at most d neighbors B A). When $$d=1$$ , this MATCHING CUT problem. Gomes and Sau [9] gave first fixed-parameter tractable algorithm for parameterized by maximum number crossing edges cut (i.e., size edge cut). However, their paper ...

Luca Trevisan [1] presented an approximation algorithm for Max Cut based on spectral partitioning techniques. He proved that the algorithm has an approximation ratio of at least 0.531. We improve this bound up to 0.6142. We also define and extend this result for the more general Maximum Colored Cut problem.

Circulating embryotoxic factors could be responsible for reproductive failures observed in patients suffering from recurrent spontaneous abortions (RSA) and endometriosis. The mouse bioassay has been widely used to detect such factors, since sera from these patients inhibit early embryonic development. This bioassay consists in the in-vitro culture of two-cell mouse embryos in the presence of d...

In this paper, we deal with (angular cut-off) Boltzmann equation soft potential ($-3<\gamma<0$). particular, construct a unique global solution in $L^\infty_{x,v}$ which converges to equilibrium asymptotically provided that initial data has large amplitude but sufficiently small relative entropy. Because frequency multiplier is not uniformly positive anymore, unlike hard case, time-involved vel...

in the open-pit mining, one of the first decisions that must be made in production planning stage, after completing the design of final pit limits, is determining of the processing plant cut-off grade. since this grade has an essential effect on operations, choosing the optimum cut-off grade is of considerable importance. different goals may be used for determining optimum cut-off grade. one of...

A graph $Gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ ‎if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$‎, ‎respectively‎. ‎Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$‎. ‎Then, $Gamma$ is said to be normal edge-transitive‎, ‎if $N_{Aut(Gamma)}(G)$ acts transitively on edges‎. ‎In this paper‎, ‎the eigenvalues of normal edge-tra...