In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph as a minor. A set of four graphs is shown to be the obstruction set of graphs with branchwidth at mo...

We present a new approach to the logic of at most, introducing the notion of parametric propositions to modal natural deduction proofs. We apply the method with a natural deduction formulation of the doxastic logic N, a new system in the “only knowing” family. Using parametric proof rules, we give introduction and elimination rules for belief at most that directly match the natural second-order...

The linear spaces on points are constructed The parameters of the geometries play an important role In order to make generation easy we construct possible parameter sets for geometries rst purely algebraically Afterwards the corresponding geometries are tried to construct We de ne line types point types point cases and also re ned line types These are the rst three steps of a general decomposit...

The structure of the initiator binding protein from the primitive eukaryote Trichomonas vaginalis reveals how a single protein can orchestrate promoter recognition, RNA polymerase II recruitment, and start site selection, and provides an evolutionary link with transcription initiation in higher eukaryotes.

We present a new data structure to index strings that is very similar to a suffix tree. The new structure indexes the factors of a string whose length does not exceed k, and only those. We call such structure the at most k-deep factor tree, or k-factor tree for short. Time and space complexities for constructing the tree are linear in the length of the string. The construction is on-line. Compa...

We provide a characterization of graphs of linear rankwidth at most 1 by minimal excluded vertex-minors.