3 Citations
Planar graphs without cycles of length from 4 to 7 are near-bipartite
- 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
- Mathematics
- 2022
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
- MathematicsJ. 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…
Decomposing a Planar Graph into an Independent Set and a 3-Degenerate Graph
- MathematicsJ. Comb. Theory, Ser. B
- 2001
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 cycles of length from 4 to 7 are 3-colorable
- MathematicsJ. Comb. Theory, Ser. B
- 2005
Planar graphs without 4,6,8-cycles are 3-colorable
- Mathematics
- 2007
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
- MathematicsDiscret. Math.
- 2016
Decomposing a planar graph of girth 5 into an independent set and a forest
- MathematicsJ. Comb. Theory, Ser. B
- 2009
Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable
- MathematicsDiscret. Math.
- 2010
Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable
- MathematicsJ. Comb. Theory, Ser. B
- 2009
Partitioning a triangle-free planar graph into a forest and a forest of bounded degree
- MathematicsElectron. Notes Discret. Math.
- 2015
On the partition of a planar graph of girth 5 into an empty and an acyclic subgraph (Russian), Diskretnyi
- Analiz i Issledovanie Operatsii,
- 2001