For ordinary graphs it is known that any graph G with more edges than the TurÃ¡n number of Ks must contain several copies of Ks, and a copy of Kâˆ’ s+1, the complete graph on s+ 1 vertices with one missing edge. ErdÅ‘s asked if the same result is true for K s , the complete 3-uniform hypergraph on s vertices. In this note we show that for small values of n, theâ€¦ (More)

The notion of a 1-vertex transfer matrix for multidimensional codes is introduced. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computationsâ€¦ (More)

A graph homomorphism from a graph G to a graph H is a mapping h : V (G)â†’ V (H) such that h(u) âˆ¼ h(v) if u âˆ¼ v. Graph homomorphisms are well studied objects and, for suitable choices of eitherG orH, many classical graph properties can be formulated in terms of homomorphisms. For example the question of wether there exists a homomorphism from G to H = Kq isâ€¦ (More)