In this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to beH-free if no graph inH is an induced subgraph of G. We completely characterize the setH such that every connected H-free graph of sufficiently large even order has a perfect matching in the foll...

We present the set of planar graphs that always have a simultaneous geometric embedding with a strictly monotonic path on the same set of n vertices, for any of the n! possible mappings. These graphs are equivalent to the set of unlabeled level planar (ULP) graphs that are level planar over all possible labelings. Our contributions are twofold. First, we provide linear time drawing algorithms f...

Let L denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set (La,⊆) is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in (La,⊆) has a finite or infinite family of minimal forbidden subgraphs.

A generalized Davenport-Schinzel sequence is one over a finite alphabet that excludes subsequences isomorphic to a fixed forbidden subsequence. The fundamental problem in this area is bounding the maximum length of such sequences. Following Klazar, we let Expσ, nq be the maximum length of a sequence over an alphabet of size n excluding subsequences isomorphic to σ. It has been proved that for e...

Weakly median graphs, being defined by interval conditions and forbidden induced subgraphs, generalize quasi-median graphs as well as pseudo-median graphs. It is shown that finite weakly median graphs can be decomposed with respect to gated amalgamation and Cartesian multiplication into 5-wheels, induced subgraphs of hyperoctahedra (alias cocktail party graphs), and 2-connected bridged graphs n...

Human society and its religions and cultures have laid out numerous guidelines, often involving dietary restrictions (Deut. 14:4-5; Lev. 11:2-7). One such set of restrictions still observed by many Jews today relates to the distinction between pure and impure, edible and forbidden mammals (Talmud Bavli, Avoda Zara 35b). The ancient Jewish dietary laws (kashrut) have often perplexed both gentile...

Suppose a graph G have n vertices, m edges, and t triangles. Letting λn (G) be the largest eigenvalue of the Laplacian of G and μn (G) be the smallest eigenvalue of its adjacency matrix, we prove that λn (G) ≥ 2m2 − 3nt m (n2 − 2m) , μn (G) ≤ 3n3t− 4m3 nm (n2 − 2m) , with equality if and only if G is a regular complete multipartite graph. Moreover, if G is Kr+1-free, then λn (G) ≥ 2mn (r − 1) (...

Gatifloxacin is an antibacterial agent belonging to the fourth-generation fluoroquinolone family. Four piperazine-linked fluoroquinolone dimers of Gatifloxacin were observed during the laboratory process for Gatifloxacin and they were identified. The present work describes the origin, synthesis, characterization, and control of these dimers along with the synthesis of Despropylene Gatifloxacin ...

A convexity structure satisfies the separation property 5'4 if any two disjoint convex sets extend to complementary half-spaces. This property is investigated for alignment spaces, n-ary convexities, and graphs. In particular, it is proven that a) an n-ary convexity is $4 iff every pair of disjoint polytopes with at most n vertices can be separated by complementary half spaces, and b) an interv...

Many graphs which are encountered in the study of graph theory are characterized by a type of configuration or subgraphs they possess. However, there are occasions when such graphs are more easily defined or described by the kind of subgraphs they are not permitted to contain. Such subgraphs are called forbidden subgraphs. In this paper, we present characterizations of graphs whose blict and bl...