Length-Bounded Cuts: Proper Interval Graphs and Structural Parameters

We study the Length-Bounded Cut problem for special graph classes and from a parameterized complexity viewpoint. Here, we are given G, two vertices s t, positive integers β λ. The task is to find set F of at most edges such that each s-t-path length λ in G contains some edge F. Bazgan et al. [20] conjectured admits polynomial-time algorithm if input proper interval graph. confirm this conjecture by providing dynamic-programming-based algorithm. Moreover, strengthen W[1]-hardness result Dvořák Knop [15] pathwidth showing combined parameter maximum degree Finally, prove W[1]-hard feedback vertex number. Both our hardness results complement known XP algorithms.