A multipartite or c-partite tournament is an orientation of a complete c-partite graph. Lu and Guo (submitted for publication) [3] recently introduced strong quasi-Hamiltonianconnectivity of a multipartite tournament D as follows: For any two distinct vertices x and y ofD, there is a pathwith at least one vertex from each partite set ofD from x to y and from y to x. We obtain the definition for...

— It is an intriguing question to see what kind of information on the structure of an oriented graph D one can obtain if D does not contain a fixed oriented graph H as a subgraph. The related question in the unoriented case has been an active area of research, and is relatively well-understood in the theory of quasi-random graphs and extremal combinatorics. In this paper, we consider the simple...

We define the intersection complex for universal cover of a compact weakly special square and show that it is quasi-isometry invariant. By using this invariant, we study quasi-isometric classification 2-dimensional right-angled Artin groups planar graph 2-braid groups. Our results two well-known cases groups: (1) those whose defining graphs are trees (2) outer automorphism finite. Finally, ther...

First, we show that a warped product of line with Riemannian manifold (fiber) is weakly conformally flat and quasi Einstein if only the fiber in which case Bach flat. Finally, characterize classify contact manifolds satisfying (and doubly weakly) quasi-Einstein ( $$\eta $$ -Einstein) conditions.

We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weakly quasi-o-minimal, and P -minimal theories.