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 ...

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 ...

This is a preview. Log in through your library . Abstract We introduce a new model for the infection of one or more subjects by a single agent, and calculate the probability of infection after a fixed ...