Polynomial kernelization for Conflict-Free Edge Cut parameterized by vertex cover

Determine whether Conflict-Free Edge Cut admits a polynomial kernel when parameterized by the vertex cover number of the primary graph.

Background

The paper studies Conflict-Free Edge Cut, which asks whether a connected undirected primary graph has an edge cut that is an independent set in a conflict graph whose vertices represent the primary graph's edges. It establishes a polynomial-kernelization lower bound for the minimum-size variant of Conflict-Free Edge Cut when parameterized by the vertex cover number of the primary graph.

The authors explicitly note that this lower bound does not automatically apply to the non-minimization existence variant, leaving the polynomial-kernelization status of Conflict-Free Edge Cut under the vertex-cover parameter unresolved.