Planar graphs without short even cycles are near-bipartite

Runrun Liu; Gexin Yu

DOI:10.1016/j.dam.2020.04.017
Corpus ID: 219061364

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}
}

Runrun Liu, Gexin Yu
Published 25 April 2020
Mathematics
Discret. Appl. Math.

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4 Citations

Background Citations

Planar graphs without cycles of length from 4 to 7 are near-bipartite

Lili Hao, Weihua Yang, Shuang Zhao
Mathematics
2022

: 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…

Planar graphs without normally adjacent short cycles

Fangyao Lu, Mengjiao Rao, Qian-qian Wang, Tao Wang
Mathematics
Discret. Math.
2022

A sufficient condition for a planar graph to be <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e20" altimg="si12.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="script">F</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="script">F</mml:mi></mml

Runrun Liu, Weifan Wang
Computer Science
Discrete Applied Mathematics
2022

References

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Decomposing a Planar Graph into Degenerate Graphs

C. Thomassen
Mathematics
J. Comb. Theory, Ser. B
1995

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…