Let k be a natural number. We introduce k-threshold graphs. We show that there exists anO(n) algorithm for the recognition of k-threshold graphs for each natural number k. k-Threshold graphs are characterized by a finite collection of forbidden induced subgraphs. For the case k = 2 we characterize the partitioned 2threshold graphs by forbidden induced subgraphs. We introduce restricted, and spe...

Additive manufacturing (AM) has the potential to create geometrically complex parts that require a high degree of customization, using less material and producing less waste. Recent studies have shown that AM can be an economically viable option for use by the industry, yet there are some inherent challenges associated with AM for wider acceptance. The lack of standards in AM impedes its use fo...

We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.

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.