We construct a polynomial-time algorithm to approximate the branch-width of certain symmetric submodular functions, and give two applications. The first is to graph “clique-width”. Clique-width is a measure of the difficulty of decomposing a graph in a kind of tree-structure, and if a graph has clique-width at most k then the corresponding decomposition of the graph is called a “k-expression”. ...

this study was carried out in order to determine the leave characteristics of some chestnut genotypes in the central black sea region of turkey and also to determine whether the leaf morphometric characteristics could be used for differentiation of genotypes. in this study, seven chestnut (castanea sativa mill.) genotypes (sa5-1, se 3-12, se 21-2, se 21-9, 552-8, 556-7 and 556-8) and one cultiv...

Monoidal width was recently introduced by the authors as a measure of complexity decomposing morphisms in monoidal categories. We have shown that category cospans graphs, and its variants can be used to capture tree width, path branch width. In this paper we study matrices, an extension different open where connectivity information is handled with matrix algebra graphs are composed along edges ...

background and aims. various methods are used to measure the size and form of the teeth, including the golden proportion, and the width-to-length ratio of central teeth, referred to as the golden standard. the aim of this study was to evaluate the occurrence of golden standard values and golden proportion in the anterior teeth. materials and methods. photographs of 100 dentistry students (50 ma...

A bubble model is a 2-dimensional representation of proper interval graphs. We consider proper interval graphs that have bubble models of specific properties. We characterise the maximal such proper interval graphs of bounded clique-width and of bounded linear cliquewidth and the minimal such proper interval graphs whose clique-width and linear cliquewidth exceed the bounds. As a consequence, w...

the biologic width (bw) includes attached epithelial cells and connective tissue attachment complex being very important in the periodontal health during prosthetic treatments as invading this zone can cause bone resorption and gingival recession. the present study investigated biologic width values in the normal periodontium in anterior and posterior teeth. 30 patients that referred from resto...