A graph is (I,F)-colorable if its vertex set can be partitioned into two subsets, one of which is an independent set, and the other induces a forest. In this paper, we prove that every planar graph without 5−-cycles at distance less than 3 is (I,F)-colorable.
@article{arxiv.2311.02969,
title = {Planar graphs without $5^{-}$-cycles at distance less than $3$ are $(\mathcal{I}, \mathcal{F})$-colorable},
author = {Zhen He and Tao Wang and Xiaojing Yang},
journal= {arXiv preprint arXiv:2311.02969},
year = {2023}
}