A linear k-forest is a graph whose components are paths with lengths at most k. The minimum number of linear k-forests needed to decompose a graph G is the linear k-arboricity of G and denoted by ...

Abstract Forty years ago, Kleitman considered the numbers of crossings in good planar drawings of the complete bipartite graph ${K_{m,n}}$. Among other things, he ...

Anti-Ramsey theory in graphs is a branch of combinatorial mathematics that examines the conditions under which a graph, when its edges are coloured, must necessarily contain a ‘rainbow’ subgraph – a ...