For a graphG = (V,E), let bc(G) denote the minimum number of pairwise edge disjoint complete bipartite subgraphs of G so that each edge of G belongs to exactly one of them. It is easy to see that for every graph G, bc(G) ≤ n−α(G), where α(G) is the maximum size of an independent set of G. Erdős conjectured in the 80s that for almost every graph G equality holds, i.e., that for the random graph ...

In this work, we improve a previously developed segmentation scheme aimed at extracting edge information from speckled images using a maximum likelihood edge detector. The scheme was based on finding a threshold for the probability density function of a new kernel defined as the arithmetic mean-to-geometric mean ratio field over a circular neighborhood set and, in a general context, is founded ...

Motivated by a problem that arises in the study of mirrored storage systems, we describe, for any fixed , δ > 0 and any integer d ≥ 2, explicit or randomized constructions of d-regular graphs on n > n0( , δ) vertices in which a random subgraph obtained by retaining each edge, randomly and independently, with probability ρ = 1− d−1 , is acyclic with probability at least 1 − δ. On the other hand ...

processing have been supported by the Danish National Research Foundation. Abstract A new edge detector for polarimetric SAR data has been developed. The edge detector is based on a newly developed test statistic for equality of two complex covariance matrices following the complex Wishart distribution and an associated asymptotic probability for the test statistic. The new polarimetric edge de...

We de ne a space of random edge-coloured graphs Gn;m; which correspond naturally to edge -colourings of Gn;m. We show that there exist constants K0; K1 21 such that provided m K0n logn and K1n then a random edge coloured graph contains a multi-coloured Hamilton cycle with probability tending to 1, as the number of vertices n tends to in nity.

We propose a statistical approach to combining edge cues at multiple scales using data driven probability distributions. These distributions are learnt on the Sowerby and South Florida datasets which include the ground truth positions of edges. We evaluate our results using Chernoff information and conditional entropy. Our results demonstrate the effectiveness of multi-scale processing and vali...

‎‎let $g=(v,e)$ be a simple graph‎. ‎an edge labeling $f:eto {0,1}$ induces a vertex labeling $f^+:vtoz_2$ defined by $f^+(v)equiv sumlimits_{uvin e} f(uv)pmod{2}$ for each $v in v$‎, ‎where $z_2={0,1}$ is the additive group of order 2‎. ‎for $iin{0,1}$‎, ‎let‎ ‎$e_f(i)=|f^{-1}(i)|$ and $v_f(i)=|(f^+)^{-1}(i)|$‎. ‎a labeling $f$ is called edge-friendly if‎ ‎$|e_f(1)-e_f(0)|le 1$‎. ‎$i_f(g)=v_f(...

In Chung-Lu random graphs, a classic model for real-world networks, each vertex is equipped with a weight drawn from a power-law distribution (for which we fix an exponent 2 < β < 3), and two vertices form an edge independently with probability proportional to the product of their weights. Modern, more realistic variants of this model also equip each vertex with a random position in a specific ...

Motivated by experiments on splitting one-dimensional quasicondensates, we study the statistics of the work done by a quantum quench in a bosonic system. We discuss the general features of the probability distribution of the work and focus on its behavior at the lowest energy threshold, which develops an edge singularity. A formal connection between this probability distribution and the critica...

We consider semirandom graph models for nding large independent sets, colorings and bisections in graphs. These models generate problem instances by blending random and adversarial decisions. To generate semirandom independent set problems, an independent set S of n ver-tices is randomly chosen. Each edge connecting S with S is chosen with probability p, and an adversary is then allowed to add ...