Disjoint blocking sets in cycle systems
An \(m\)-cycle system of order \(n\) is a collection of cycles of length \(m\) which partition the edge set of the complete graph \(K_n\). Given an \(m\)-cycle system, a blocking set is a set of vertices that intersects all cycles and does not contain any cycle. A partition of the vertex set into \(k\) sets such that every set intersects all cycles is called a strong \(k\)-coloring. (A blocking set is a strong 2-coloring.) The authors use constructive and nonconstructive methods to prove various existence results for strongly \(k\)-colorable \(m\)-cycle systems.
scientific article; zbMATH DE number 1369800