On Minimal k‐Factor‐Critical Planar Graphs
Qiuli Li, Fuliang Lu, Heping Zhang · Journal of Graph Theory · 2026
ABSTRACT A graph of order is said to be ‐factor‐critical () if the removal of any vertices results in a graph with a perfect matching. A ‐factor‐critical graph is minimal if is not ‐factor‐critical for any edge in . Favaron and Shi posed the conjecture that every minimal ‐factor‐critical graph is of minimum degree in 1998. In this paper, we confirm the conjecture for planar graphs.