Increasing paths in edge-ordered graphs: the hypercube and random graphs
Jessica De Silva, Theodore Molla, Florian Pfender, Troy Retter, Michael B. Tait · arXiv (Cornell University) · 2015
An edge-ordering of a graph $G=(V,E)$ is a bijection $ϕ:E\to\{1,2,...,|E|\}$. Given an edge-ordering, a sequence of edges $P=e_1,e_2,...,e_k$ is an increasing path if it is a path in $G$ which satisfies $ϕ(e_i)