Graph homomorphisms and chromatic numbers are foundational concepts in modern graph theory, with widespread applications that extend from combinatorial optimisation to theoretical computer science. A ...

A k-graph is an ordered couple (V, E) where V is a set and E a set of k-tuples of elements of V; thus, a 2-graph is an ordinary graph. If the notions of the independent set and the chromatic number ...

It is shown that for arbitrary positive integers $m, n$ there exists a $\phi(m, n)$ such that if $\chi(G) \geqslant \phi(m, n)$, then $G$ contains either a complete ...