We study the problem of finding, in a directed graph, an st-walk of length r mod q which is
edge-minimum, ie, uses the smallest number of distinct edges. Despite the vast literature on …

This note summarizes the state of what is known about the tractability of the problem
ModPath, which asks if an input undirected graph contains a simple st-path whose length …

For a finite abelian group A, define f (A) to be the minimum integer such that for every
complete digraph Γ on f vertices and every map w: E (Γ)→ A, there exists a directed cycle C …

For a finite (not necessarily Abelian) group $(\Gamma,\cdot) $, let $ n (\Gamma)\in\mathbb
{N} $ denote the smallest positive integer $ n $ such that for every labelling of the arcs of the …

For a finite Abelian group $(\Gamma,+) $, let $ n (\Gamma) $ denote the smallest positive
integer $ n $ such that for each labelling of the arcs of the complete digraph of order $ n …

For a finite abelian group $ A $, define $ f (A) $ to be the minimum integer such that for every
complete digraph $\Gamma $ on $ f $ vertices and every map $ w: E (\Gamma)\rightarrow A …