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math.CO2025
Approximating temporal modularity on graphs of small underlying treewidth
Vilhelm Agdur, Jessica Enright, Laura Larios-Jones +3
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to…
math.CO2025
Tangled Paths: A Random Graph Model from Mallows Permutations
Jessica Enright, Kitty Meeks, William Pettersson +1
We introduce the random graph which results from taking the union of two paths of length , where the vertices of one of the paths have been relabelled a…
math.CO2025
Directed branch-width: A directed analogue of tree-width
Benjamin Merlin Bumpus, Kitty Meeks, William Pettersson
Gurski and Wanke showed that a graph class C has bounded tree-width if and only if its associated class of directed line graphs has bounded clique-width. Inevitably -- asking wheth…