We completely determine the complexity status of the 3-colorability problem for hereditary graph classes defined by two forbidden induced subgraphs with at most five vertices. © 2015 Elsevier B.V. All rights reserved.

In the study of full bubble model graphs of bounded clique-width and bounded linear clique-width, we determined complete sets of forbidden induced subgraphs, that are minimal in the class of full bubble model graphs. In this note, we show that (almost all of) these graphs are minimal in the class of all graphs. As a corollary, we can give sets of minimal forbidden induced subgraphs for graphs o...

Forbidden minors and subdivisions for toroidal graphs are numerous. In contrast, the toroidal graphs with no K3,3’s have a nice explicit structure and short lists of obstructions. For these graphs, we provide the complete lists of four forbidden minors and eleven forbidden subdivisions.

A graph is 1-extendible if every edge has a 1-factor containing it. A 1-extendible non-bipartite graph G is said to be near bipartite if there exist edges e1 and e2 such that G − {e1, e2} is 1-extendible and bipartite. We characterise the Pfaffian near bipartite graphs in terms of forbidden subgraphs. The theorem extends an earlier characterisation of Pfaffian bipartite graphs.

We analyze the structure of reduced expressions in the Coxeter groups An, Bn and Dn. Several special classes of elements are singled out for their connections with symmetric functions or the theory of P -partitions. Membership in these special classes is characterized in a variety of ways, including forbidden patterns, forbidden subwords, and by the form of canonically chosen reduced words.

We introduce and study a class of simplicial complexes, the orphan complexes, associated to simple graphs whose family of (open or closed) vertex-neighborhoods are anti-Sperner. Under suitable restrictions, we show that orphan complexes of such graphs are always shellable and provide a characterization of graphs in terms of induced forbidden subgraphs contained in this restricted subfamily.

In this paper we demonstrate that several theorems from [1] and [3] do not hold as they are stated. These are the theorems regarding forbidden subposet characterizations of certain classes of coverincomparability graphs. In this paper we correct a mistake in the main theorem of [1], reformulate the corresponding statements and present corrected proofs. We further characterize posets whose cover...

background: domestic and industrial wastewaters are mostly treated by biological process such as activated sludge, aerobic pond, and anaerobic treatment. this study focuses on characterizing the quality of sewage sludge in the sultanate of oman chosen from three industrial sewage treatment plants (stps): rusayl industrial estate (rsl.ie); sohar industrial estate (sie); and raysut industrial est...

this study is devoted to the morphological, chemical and physical characterization of raw material of the fruit of luffa cylindrica. by microscopic analysis, it can be observed that the fruit is composed of an assembly of dependent cords, where four parts are differentiated: external, internal wall, core and bond. each cord consists of hollow and flexible cylindrical fibers.the external part is...

the effects of different sources of carbon, nitrogen and some of trace elements on cultivation of bacillus thuringiensis h14 were studied. glucose, glycerol, sodium acetate, (nh4)2so4, corn steep liquor, yeast extract, hydrolyzed casein, ca2+, mg2+ and mn2+ were the main parameters evaluated by plackett-burman statistical method. all elements have insignificant effect on germination while spore...