In this paper, we prove that an element splitting operation by every pair of elements on a cographic matroid yields a cographic matroid if and only if it has no minor isomorphic to M(K4).

The G-width of a class of graphs G is defined as follows. A graph G has G-width k if there are k independent sets N1, . . . ,Nk in G such that G can be embedded into a graph H ∈ G such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in Ni. For the class TH of threshold graphs we show that TH-width is NP-complete and we present fixed-para...

Given a class of graphs F , a forbidden subgraph characterization (FSC) is a set of graphs H such that a graph G belongs to F if and only if no graph of H is isomorphic to an induced subgraph of G. FSCs play a key role in graph theory, and are at the center of many important results obtained in that field. In this paper, we present novel methods that automate the generation of conjectures on FS...

For an arbitrary fixed surface S, a linear time algorithm is presented that for a given graph G either finds an embedding of G in S or identifies a subgraph of G that is homeomorphic to a minimal forbidden subgraph for embeddability in S. A side result of the proof of the algorithm is that minimal forbidden subgraphs for embeddability in S cannot be arbitrarily large. This yields a constructive...

Given a graph G = (V; E), the metric polytope S(G) is deened by the inequalities x(F) ? x(C n F) jFj ? 1 for F C; jFj odd ; C cycle of G, and 0 x e 1 for e 2 E. Optimization over S(G) provides an approximation for the max-cut problem. The graph G is called 1 d-integral if all the vertices of S(G) have their coordinates in f i d j 0 i dg. We prove that the class of 1 d-integral graphs is closed ...

1 Abstract—Nowadays, to achieve competitive advantage, the industrial companies are considering that success is sustained to great product development. That is to manage the product throughout its entire lifecycle. Achieving this goal requires a tight collaboration between actors from a wide variety of domains, using different software tools producing various product data types and formats. The...

1 Corresponding Author ABSTRACT In order to reduce product development time, we need software tools that can perform automated validation of the proposed design concepts. These tools will ensure that only valid design concepts are transferred to the detailed design stage for further development. This paper provides a step towards the automated validation of proposed design concepts. We define t...

The aim of the 2005-06 NKS-B NordRisk project has been to present practical methods for probabilistic risk assessment from long-range atmospheric transport and deposition of radioactive material. In this project an atlas of long-range atmospheric dispersion and deposition patterns derived from archived numerical weather prediction (NWP) model data coupled to an atmospheric dispersion model has ...

The term “Business Model”started to gain momentum in the early rise of the new economy and it is currently used both in business practice and scientific research. Under a general point of view BMs are considered as a contact point among technology, organization and strategy used to describe how an organization gets value from technology and uses it as a source of competitive advantage. Recent c...

In this tutorial, we explore open source software practices and tools that are suitable for a growing number of creators of interactive and playful systems. The introduction of open source tools such as Processing and Arduino has motivated a broader participation of technical and non-technical users in the creative production of interactive systems. Maker communities meet regularly and they sha...