In this thesis we consider ordered graphs (that is, graphs with a fixed linear ordering on their vertices). We summarize and further investigations on the number of edges an ordered graph may have while avoiding a fixed forbidden ordered graph as a subgraph. In particular, we take a step toward confirming a conjecture of Pach and Tardos [12] regarding the number of edges allowed when the forbid...

Clique-width is a graph parameter with many algorithmic applications. For a positive integer k, the k-th power of a graph G is the graph with the same vertex set as G, in which two distinct vertices are adjacent if and only if they are at distance at most k in G. Many graph algorithmic problems can be expressed in terms of graph powers. We initiate the study of graph classes of power-bounded cl...

We prove a precise characterization of toroidal graphs with no K3,3-subdivisions in terms of forbidden minors and subdivisions. The corresponding lists of four forbidden minors and eleven forbidden subdivisions are shown.

An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let La denote a class of all such properties. In the paper, we consider Hreducible over La properties with H being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.

We investigate which switching classes do not contain a bipartite graph. Our final aim is a characterization by means of a set of critically non-bipartite graphs: they do not have a bipartite switch, but every induced proper subgraph does. In addition to the odd cycles, we list a number of exceptional cases and prove that these are indeed critically non-bipartite. Finally, we give a number of s...

The Gram dimension gd(G) of a graph is the smallest integer k ≥ 1 such that, for every assignment of unit vectors to the nodes of the graph, there exists another assignment of unit vectors lying in R, having the same inner products on the edges of the graph. The class of graphs satisfying gd(G) ≤ k is minor closed for fixed k, so it can characterized by a finite list of forbidden minors. For k ...

The applicability of Nkel's pair model to metallic 3d surfaces and interfaces is explained in terms of the tight-binding momentstheorem. The Nee1 model reproduces itinerant magnetism so long as the band structure is approximated by third-moment atomic-pair contributions. This establishes an atomic NCel description of interfaces and impurities. The NCel parameter g depends on the d-band filling ...

Muon spin relaxation measurements in iron-oxypnictide systems have revealed: (1) commensurate long-range order in undoped LaFeAsO; (2) a Bessel function line shape in LaFeAs(O0.97F0.03) which indicates possible incommensurate or stripe magnetism; (3) anomalous weak magnetism existing in superconducting LaFePO, CeFeAs(O0.084F0.16), and NdFeAs(O0.88F0.12) but absent in superconducting LaFeAs(O0.9...

M a g n e t i c f i e l d s a r e u b i q u i t o u s i n t h e U n i v e r s e b e c a u s e o f t h e a b s e n c e (o r r a r i t y ) o f f r e e m a g n e t i c m o n o p o l e s . However , t h e l a r g e s c a l e c o n c e n t r a t i o n of m a g n e t i c f l u x i n an e s s e n t i a l l y n o n f e r r o m a g n e t i c body s u c h a s t h e E a r t h , r e q u i r e s a n o n c o...

Electrical networks are defined and a definition of when a bond graph and an electrical network are equivalent is given. Bond graphs and electrical networks are defined to be primitive if they contain no transformers or gyrators. A bond graph is defined to be realisable if it is equivalent to an electrical network and primitively realisable if it is equivalent to a primitive electrical network....