A Congestion Parameter for Depth-First Graph Traversals (opens in new tab)

We explore a new graph parameter, the KLX number, which quantifies the minimum edge congestion of depth-first search (DFS) traversals of a given graph. Originally motivated by a problem in RNA nanostructure design, this parameter is also of independent theoretical interest. Informally, the KLX number of a graph is defined as the minimum, over all its DFS traversals, of the maximum number of back edges that are simultaneously open during the trav...