On globally sparse Ramsey graphs

We say that a graph $G$ has the Ramsey property w.r.t.\ some graph $F$ and some integer $r\geq 2$, or $G$ is $(F,r)$-Ramsey for short, if any $r$-coloring of the edges of $G$ contains a monochromatic copy of $F$. R{\"o}dl and Ruci{\'n}ski asked how globally sparse $(F,r)$-Ramsey graphs $G$ can possibly be, where the density of $G$ is measured by the subgraph $H\subseteq G$ with the highest average degree. So far, this so-called Ramsey density is known only for cliques and some trivial graphs $F$. In this work we determine the Ramsey density up to some small error terms for several cases when $F$ is a complete bipartite graph, a cycle or a path, and $r\geq 2$ colors are available

Some colouring problems for Paley graphs

The Paley graph Pq, where q≡1(mod4) is a prime power, is the graph with vertices the elements of the finite field Fq and an edge between x and y if and only if x-y is a non-zero square in Fq. This paper gives new results on some colouring problems for Paley graphs and related discussion. © 2005 Elsevier B.V. All rights reserved

Multiple Camera Considerations in a View-Dependent Continuous Level of Detail

We introduce the Camera Aware View-dEpendent Continuous Level Of Detail (CAVECLOD) polygon mesh representation. Several techniques recently have been developed that use a hierarchy of vertex split and merge operations to achieve continuous LOD. These techniques exploit temporal coherence. However, when multiple cameras are simultaneously viewing a polygon mesh at continuous LOD, the exploitation of temporal coherence is difficult. The CAVECLOD mesh representation enables multiple cameras to simultaneously exploit temporal coherence. Texture coordinates and normal vectors are preserved and the algorithm uses Microsoft DirectX Vertex Buffers and Index Buffers for efficient rendering. Interactive frame rates are achieved on large models on commercially available hardware