We present a matrix multiplication based algorithm for counting the number of (induced) occurrences of a fixed r-uniform hypergraph in a larger hypergraph. In many cases, the running time is better than that of the näıve algorithm. We also present several useful applications of the algorithm, such as determining the dominant color among monochromatic simplices in a redblue edge-colored hypergra...

In this talk we will discuss some examples of graph homomorphisms. More precisely, the graph parameters which can be represented by counting the graph homomorphisms. The main reference is Section 2 in [2].

For a graph G, let     max : is an edge cut of b G D D G  . For graphs G and H, a map     :V G V H   is a graph homomorphism if for each   e uv E G   ,       u v E H    . In 1979, Erdös proved by probabilistic methods that for p ≥ 2 with

A graph homomorphism is a vertex map which carries edges from a source graph to edgesin a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem(MAX H -COL) are edge-weighted graphs G and the objective is to find a subgraph of G that hasmaximal total edge weight, under the condition that the subgraph has a homomorphism to H ;note that for H = Kk th...

For every hypergraph on n vertices there is an associated subspace arrangement in R n called a hypergraph arrangement. We prove shellability for the intersection lattices of a large class of hypergraph arrangements. This class incorporates all the hypergraph arrangements which were previously shown to have shellable intersection lattices.

Following the last talk on graph homomorphisms, we continue to discuss some examples of graph homomorphisms. But this time we will focus on some models, that is, the homomorphism G → H for the graph H with fixed weights. The main reference is Section 1 in [2].