In early 70s Berge conjectured that any bridgeless cubic graph contains five perfect matchings such that each edge belongs to at least one of them. In 1972 Fulkerson conjectured that, in fact, we can find six perfect matchings containing each edge exactly twice. By introducing the concept of an r-graph (a remarkable generalization of one of bridgeless cubic graph) Seymour in 1979 conjectured th...

We consider the size of circuits that perfectly hash an arbitrary subset S⊂{0, 1} of cardinality 2 into {0, 1}. We observe that, in general, the size of such circuits is exponential in 2k−m, and provide a matching upper bound.

We give various reformulations of the Strong Perfect Graph Conjecture, based on a study of forced coloring procedures, uniquely colorable subgraphs and ! ? 1-cliques in minimal imperfect graphs.

The amount of at retrieval time is one of the when looking for such functioiis. evidence about the effectivensss reduce the memory requirements perfect hash function proposed

A brief summary of results on homotheties in General Relativity is given, including general information about space-times admitting an r-parameter group of homothetic transformations for r > 2, as well as some specific results on perfect fluids. Attention is then focussed on inhomogeneous models, in particular on those with a homothetic group H 4 (acting multiply transitively) and H 3. A classi...

The mod $p$ Riemann-Hilbert correspondence (in covariant and contravariant forms) relates $\mathbb{F}_p$-\'etale sheaves on the spectrum of an $\mathbb{F}_p$-algebra $R$ Frobenius modules over $R$. We give exposition these correspondences using Breen's vanishing results perfect site.

‎Unmixed bipartite graphs have been characterized by Ravindra and‎ ‎Villarreal independently‎. ‎Our aim in this paper is to‎ ‎characterize unmixed $r$-partite graphs under a certain condition‎, ‎which is a generalization of Villarreal's theorem on bipartite‎ ‎graphs‎. ‎Also, we give some examples and counterexamples in relevance to this subject‎.

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...