We investigate the enumerative aspects of various classes of perfect graphs like cographs, split graphs, trivially perfect graphs and threshold graphs. For subclasses of permutation graphs like cographs and threshold graphs we also determine the number of permutations of f1; 2; : : : ; ng such that the permutation graph G] belongs to that class. We establish an interesting bijec-tion between pe...

We introduce a new way of specifying graphs: through languages, i.e., sets of strings. The strings of a given (finite, prefix-free) language represent the vertices of the graph; whether or not there is an edge between the vertices represented by two strings is determined by the pair of symbols at the first position in these strings where they differ. With this new, ``positional'' or lexicograph...

This paper is interested in independent sets (or equivalently, cliques) uniform random cographs. We also study their permutation analogs, namely, increasing subsequences separable permutations. First, we prove that, with high probability as \(n\) gets large, the largest set a cograph vertices has size \(o(n)\). answers question of Kang, McDiarmid, Reed and Scott. Using connection between graphs...

Let G be a graph. The independence-domination number γ(G) is the maximum over all independent sets I in G of the minimal number of vertices needed to dominate I. In this paper we investigate the computational complexity of γ(G) for graphs in several graph classes related to cographs. We present an exact exponential algorithm. We also present a PTAS for planar graphs.

A graph is a cograph if it does not contain 4-vertex path as an induced subgraph. An $(s, k)$-polar partition of $G$ $(A, B)$ its vertex set such that $A$ induces complete multipartite with at most $s$ parts, and $B$ the disjoint union $k$ cliques no other edges. said to be admits partition. The concepts \infty)$-, $(\infty, k)$-, \infty)$-polar graphs can analogously defined. Ekim, Mahadev de ...

In this paper we study the class of weakly quasi-threshold graphs that are obtained from a vertex by recursively applying the operations (i) adding a new isolated vertex, (ii) adding a new vertex and making it adjacent to all old vertices, (iii) disjoint union of two old graphs, and (iv) adding a new vertex and making it adjacent to all neighbours of an old vertex. This class contains the class...

In a graph coloring, each color class induces a disjoint union of isolated vertices. A graph subcoloring generalizes this concept, since here each color class induces a disjoint union of complete graphs. Erd˝ os and, independently, Albertson et al., proved that every graph of maximum degree at most 3 has a 2-subcoloring. We point out that this fact is best possible with respect to degree constr...

We show that there are polynomial-time algorithms to compute maximum independent sets in the categorical products of two cographs and two splitgraphs. The ultimate categorical independence ratio of a graph G is defined as limk→∞ α(G )/n. The ultimate categorical independence ratio is polynomial for cographs, permutation graphs, interval graphs, graphs of bounded treewidth and splitgraphs. When ...

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s, k)-polar if there exists a partition A, B of its vertex set such that A induces a complete s-partite graph (i.e., a collection of at most s disjoint stable sets with complete links between all sets) and B a disjoint union of at most k cliques (i....

The mechanism of inactivation of rodent ornithine decarboxylase by a-difluoromethylornithine (DFMO) was studied using the inhibitor labelled with 14C in both the 1 and the 5 positions. [1-14C]DFMO was a substrate and was decarboxylated by the enzyme yielding '4CO2. A radioactive metabolite derived from [5-'4C]DFMO was bound to the enzyme, and the extent of binding paralleled the irreversible in...