7 A homogeneous set of a graph G is a set X of vertices such that 2 ≤ |X| < |V (G)| 8 and no vertex in V (G) − X has both a neighbor and a non-neighbor in X. A graph 9 is prime if it has no homogeneous set. We present an algorithm to decide whether a 10 class of graphs given by a finite set of forbidden induced subgraphs contains infinitely 11 many non-isomorphic prime graphs. 12

In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M .

A semigroup is amiable if there is exactly one idempotent in each R⇤-class and in each L⇤-class. A semigroup is adequate if it is amiable and if its idempotents commute. We characterize adequate semigroups by showing that they are precisely those amiable semigroups which do not contain isomorphic copies of two particular nonadequate semigroups as subsemigroups.

Many factors influence the near-field visualization of plasmonic structures that are based on perforated elliptical slits. Here, characterization errors are experimentally analyzed in detail from both fabrication and measurement points of view. Some issues such as geometrical parameter, probe-sample surface interaction, misalignment, stigmation, and internal stress, have influence on the final ...

For various graph-theoretic properties P that impose upper bounds on the minimum degree or the size of a neighbourhood set, we characterize the class %(P’) (%((P’)) of graphs G such that G and all its subgraphs (subcontractions) have property P. For example, if P is “6 <xn” (6 = minimum degree, n = number of vertices, 0 <X < 1) then S(P’) = F(K,+,), the class of graphs that do not have K,,, as ...

We study which infinite posets have simple cofinal subsets such as chains, or decompose canonically into such subsets. The posets of countable cofinality admitting such a decomposition are characterized by a forbidden substructure; the corresponding problem for uncountable cofinality remains open.

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.