‎let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$‎. ‎we also determine‎ ‎exact value of this parameter for the cartesian product of ...

Starting from a partitioning of an edge-weighted graph into subgraphs, we develop a method which enlarges the respective sets of vertices to produce a decomposition with overlapping subgraphs. The vertices to be added when growing a subset are chosen according to a criterion which measures the strength of connectivity with this subset. By using our method on the (directed) graph associated with...

First I want to say a few words about my graph terminology. If I want to allow loops, I use the adjective reflexive. If I want to allow multiple edges, I use multigraph. Thus, a graph has no loops and no multiple edges. I use valency rather than degree. If we say a graph is 4-valent (or tetravalent), it means it is regular of valency 4, for example. A decomposition of a graph X is a partition o...

Spectral CT is a promising new imaging modality that is able to provide spectral information of several pre-selected energy ranges in one image acquisition, which allows quantitative decomposition of multiple materials. In addition to conventional reconstruction, novel decomposition techniques should be developed to realize material separation. Decomposition of multienergy X-ray data into basis...

A good watermarking scheme should be able to perform equally well on all types of images irrespective of image contents because practically watermarking has to be applied to images of all types. In this paper, it is shown that in wavelet based spread spectrum technique, watermarking at level 1 decomposition is better for textured images while watermarking at level 2 decomposition is better for ...

In this paper we introduce semi-nice tree-decompositions and show that they combine the best of both branchwidth and treewidth. We first give simple algorithms to transform a given tree-decomposition or branch-decomposition into a semi-nice tree-decomposition. We then give two templates for dynamic programming along a semi-nice treedecomposition, one for optimization problems over vertex subset...

Today’s modern world requires a digital watermarking technique that takes the redundancy of an image into consideration for embedding a watermark. The novel algorithm used in this paper takes into consideration the redundancies of spatial domain and wavelet domain for embedding a watermark. Also, the cryptographybased secret key makes the algorithm difficult to hack and help protect ownership. ...

Because existing image abstraction systems can hardly incorporate with the changing light, we present an integrated image abstraction and relighting rendering system, which is based on a salient edge-guided luminance field optimization approach. For an input image, we first adopt a sparsity prior-based illumination decomposition method to remove its original illumination and have an intrinsic i...

I discuss low dimensional incarnations of cohomology and illustrate how basic cohomological principles lead to a proof of Sperner’s lemma. CONTENTS 1. Chains and cochains with Z/2-coefficients 1 2. Application to Sperner Lemma 4 3. Where is the cohomology? 6 4. What next? 8 References 8 1. CHAINS AND COCHAINS WITH Z/2-COEFFICIENTS To keep the formalism at a minimum I will concentrate only on tr...