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...

In this paper, we present characterizations of pairs of graphs whose join graphs are 2-minimally nonouterplanar. In addition, we present a characterization of pairs of graphs whose join graphs are 2-minimally nonouterplanar in terms of forbidden subgraphs.

For the family of graphs with xed-size vertex cover k, we present all of the forbidden minors (obstructions), for k up to ve. We derive some results, including a practical nite-state recognition algorithm, needed to compute these obstructions.

A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color is equal to the maximum number of cliques of H with a common vertex, for every induced subgraph H of G. Coordinated graphs are a subclass of perfect graphs. The list of minimal forbidden induced subgraphs for the c...

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...