Roussel and Rubio proved a lemma which is essential in the proof of the Strong Perfect Graph Theorem. We give a new short proof of the main case of this lemma. In this note, we also give a short proof of Hayward’s decomposition theorem for weakly chordal graphs, relying on a Roussel–Rubio-type lemma. We recall how Roussel–Rubio-type lemmas yield very short proofs of the existence of even pairs ...

We will extend Reed's Semi-Strong Perfect Graph Theorem by proving that unbreakable C 5-free graphs diierent from a C 6 and its complement have unique P 4-structure.

The Wonderful Lemma, that was first proved by Roussel and Rubio, is one of the most important tools in the proof of the Strong Perfect Graph Theorem. Here we give a short proof of this lemma.

This article examines the geographical corridors for the establishment of rice in seventeenth-century Dutch Guiana. One corridor of introduction is associated with the expulsion of Dutch planters from Brazil in 1644, whose slaves reestablished longstanding subsistence preferences with their exodus to the colony. Another corridor links its introduction to the African Gold Coast, where rice devel...

An (N ;n,m, {w1, . . . , wt})-separating hash family is a set H of N functions h : X −→ Y with |X| = n, |Y | = m, t ≥ 2 having the following property. For any pairwise disjoint subsets C1, . . . , Ct ⊆ X with |Ci| = wi, i = 1, . . . , t, there exists at least one function h ∈ H such that h(C1), h(C2), . . . , h(Ct) are pairwise disjoint. Separating hash families generalize many known combinator...

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...