Let c(F) be the number of perfect pairs of F and c(G) be the maximum of c(F) over all (near-) one-factorizations F of G. Wagner showed that for odd n, c(Kn) ≥ n∗φ(n) 2 and for m and n which are odd and co-prime to each other, c(Kmn) ≥ 2 ∗ c(Km) ∗ c(Kn). In this note, we establish that both these results are equivalent in the sense that they both give rise to the same lower bound.

V. Chv atal proved that no minimal imperfect graph has a small transversal, that is, a set of vertices of cardinality at most + ! 1 which meets every !-clique and every -stable set. In this paper we prove that a slight generalization of this notion of small transversal leads to a conjecture which is as strong as Berge's Strong Perfect Graph Conjecture for a very large class of graphs, although ...

This paper examines how the fertility of enslaved women was affected by the promise of freedom. Exploiting geographic variation in the effect of the Fugitive Slave Law of 1850, I demonstrate a negative correlation between fertility and the distance to freedom. This negative correlation is stronger on larger plantations but weaker when the slaveholder is a woman. A similar correlation is not pre...

In order to prove the Strong Perfect Graph Conjecture, the existence of a ”simple” property P holding for any minimal non-quasi-parity Berge graph G would really reduce the difficulty of the problem. We prove here that this property cannot be of type ”G is F-free”, where F is any fixed family of Berge graphs.

The research paper explores the impact of four skills integration approach to teach tenses at undergraduate level in Pakistani setting. study puts use a quasi-experimental method. Ninety students partook this study. Four intact classes were designated draw sample. A language proficiency test was given choose sections which are consistent terms English Language proficiency. Two groups formed gro...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

This paper describes an algorithm for the interpretation of temporal relations between events mentioned in narrative (such as which event occurs before another). These relations are decided through three different levels of linguistic concepts: aspectual information for verbs, time relations for tenses, and time relations between clauses and/or sentences. One contribution of this paper is to pr...

The notion of deductive database is generalized by extending the rst-order language, used to formulate facts, rules and constraints, to a rst-order language involving time operators. A deductive database based on such an extended language is called temporal. In this paper, we rst introduce two additional time operators, one to reference past tenses, the other to reference future tenses. Then, t...