For two given graphs F and H, the Ramsey number R(F, H) is the smallest positive integer p such that for every graph G on p vertices the following holds: either G contains F as a ...
We show that the size of the smallest depth-two N-superconcentrator is (N log2 N/ log log N). Before this work, optimal bounds were known for all depths except two. For the upper b...
: Let G be a toroidal graph without cycles of a fixed length k, and l(G) the list chromatic number of G. We establish tight upper bounds Contract grant sponsor: RGC; Contract grant...
A homomorphism from an oriented graph G to an oriented graph H is a mapping from the set of vertices of G to the set of vertices of H such that ----(u)(v) is an arc in H whenever...
The connectivity index w(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where is a real number ( = 0), and d(u) denotes the degree of the vertex u. Le...