A triangle free graph which cannot be 3 imbedded in any euclidean unit sphere

3-bounded Property in a Triangle-free Distance-regular Graph

Let Γ denote a distance-regular graph with classical parameters (D, b, α, β) and D ≥ 3. Assume the intersection numbers a1 = 0 and a2 6= 0. We show Γ is 3-bounded in the sense of the article [D-bounded distance-regular graphs, European Journal of Combinatorics(1997)18, 211-229].

On the Normal Bundle of a Sphere Imbedded in Euclidean Space1

Triangle-free Partitions of Euclidean Space

The instance of this theorem when n = 2 was proved by Ceder [1]. Komjath [4] extended Ceder's result to IR, but with the weaker conclusion that no set of the partition contains the vertices of a regular tetrahedron. Subsequently, we extended Komjath's result to arbitrary dimension n in [7], where it was proved that there is a partition of IR" into countably many sets no one of which contains n ...

Linear Weingarten hypersurfaces in a unit sphere

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

A Poincaré–type Inequality on the Euclidean Unit Sphere

We consider the second variation for the volume of convex bodies associated with the Lp Minkowski-Firey combination and obtain a Poincaré-type inequality on the Euclidean unit sphere Sn−1 . Mathematics subject classification (2010): 52A20.