Tractability is the study of computational tasks with the goal of identifying which problem classes are tractable or, in other words, efficiently solvable. The class of tractable problems is traditionally assumed to be solvable in polynomial time by a deterministic Turing machine and is denoted by P. The class contains many natural tasks such as sorting a set of numbers, linear programming (the...

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...

%'c shw that perfectly orderabk grapk Sa are q&-parity graphs by exhibiting two &lodes which are not llinked by a chordless odd chain. This proof is short and simpler than the one given by H. Meynid. A graph G = (V, E) _ is called a quasi-~&y graph if for every A s X the induced subgraph GA is a clique or contains 2 nodes x, y which are riot linked by a (chordless) odd chain in G,+ Quasi-parity...

We introduce a graph transformation which preserves the clique number. When applied to graphs containing no odd hole and no cricket (a particular graph on 5 vertices) the transformation also preserves the chromatic number. Using this transformation we derive a polynomial algorithm for the computation of the clique number of all graphs in a class which strictly contains diamond-free graphs. Furt...

A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...

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 ...