Planar graphs without short even cycles are near-bipartite

@article{Liu2020PlanarGW,
  title={Planar graphs without short even cycles are near-bipartite},
  author={Runrun Liu and Gexin Yu},
  journal={Discret. Appl. Math.},
  year={2020},
  volume={284},
  pages={626-630}
}
Planar graphs without cycles of length from 4 to 7 are near-bipartite
: A graph is near-bipartite if its vertex set can be partitioned into an independent set and a set which induces a forest. In this paper, planar graphs without cycles of length from 4 to 7 are shown
Partitioning planar graphs without 4-cycles and 6-cycles into a forest and a disjoint union of paths
In this paper, we show that every planar graph without 4-cycles and 6-cycles has a partition of its vertex set into two sets, where one set induces a forest, and the other induces a forest with

References

SHOWING 1-10 OF 15 REFERENCES
Decomposing a Planar Graph into Degenerate Graphs
We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of any planar graph can be decomposed into two sets such that one of them induces a 3-degenerate graph and the other induces
Decomposing a Planar Graph into an Independent Set and a 3-Degenerate Graph
TLDR
It is proved that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph.
Planar graphs without 4,6,8-cycles are 3-colorable
In this paper we prove that every planar graph without 4, 6 and 8-cycles is 3-colorable.
The 3-colorability of planar graphs without cycles of length 4, 6 and 9
Decomposing a planar graph of girth 5 into an independent set and a forest
On the partition of a planar graph of girth 5 into an empty and an acyclic subgraph (Russian), Diskretnyi
  • Analiz i Issledovanie Operatsii,
  • 2001
...
...