In this paper, we study the minimum size 2-edge connected spanning subgraph problem (henceforth 2EC) and show that every 3-edge connected cubic graphG = (V,E), with n = |V | allows a 2EC solution for G of size at most 7n 6 , which improves upon Boyd, Iwata and Takazawa’s guarantee of 6n 5 .

We introduce a concept of a semiextension of a cycle, and we conjecture a simple necessary and sufficient condition for its existence. It is shown that our conjecture implies a strong form of the circuit double cover conjecture. We prove that the conjecture is equivalent to its restriction to cubic graphs, and we show that it holds for every cycle which is a spanning subgraph of the given graph...

Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) andK(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan’s forty identities for Rogers-Ramanujan function...

We study hierarchies of partitions in a topological space where the interiors of the classes and their frontiers are simultaneously represented. In both continuous and discrete spaces our approach rests on tessellations whose classes are R-open sets. In the discrete case, the passage from partitions to tessellations is expressed by the Alexandrov topology and yields double resolutions. A new to...

-Ia3d bicontinuous cubic phases are interpreted as constituted of a fluid film of constant thickness supponed by the gyroid minimal surface. We first compute the gyroid structure factor. Then we decorate the surface by the film. We compute the diffracted intensities and compare to X-ray intensities measured in some lipid

It is known that every group which acts transitively on the ordered edges of the cubic tree Y3, with finite vertex stabilizer, is isomorphic to one of seven finitely presented subgroups of the full automorphism group of r3-one of which is the modular group. In this paper a complete answer is given for the question (raised by Djokovic and Miller) as to whether two such subgroups which intersect ...

We describe a general theory for the stability of the laminated mi-crostructure for martensitic crystals. Our theory has been applied to the orthorhom-bic to monoclinic transformation, the cubic to tetragonal transformation, the tetrag-onal to monoclinic transformation, and the cubic to orthorhombic transformation.