论文信息 - Planar graphs without short even cycles are near-bipartite

Planar graphs without short even cycles are near-bipartite

Abstract A graph is near-bipartite if its vertex set can be partitioned into an independent set and a set that induces a forest. It is clear that near-bipartite graphs are 3-colorable. In this note, we show that planar graphs without cycles of lengths in { 4 , 6 , 8 } are near-bipartite.

Gexin Yu | Runrun Liu

[1] Carsten Thomassen. Decomposing a Planar Graph into Degenerate Graphs , 1995, J. Comb. Theory, Ser. B.

[2] André Raspaud,et al. Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable , 2010, Discret. Math..

[3] Min Chen,et al. Planar graphs without 4,6,8-cycles are 3-colorable , 2007 .

[4] Mickaël Montassier,et al. Partitioning a triangle-free planar graph into a forest and a forest of bounded degree , 2015, Electron. Notes Discret. Math..

[5] Carsten Thomassen. Decomposing a Planar Graph into an Independent Set and a 3-Degenerate Graph , 2001, J. Comb. Theory, Ser. B.

[6] Ken-ichi Kawarabayashi,et al. Decomposing a planar graph of girth 5 into an independent set and a forest , 2009, J. Comb. Theory, Ser. B.

[7] André Raspaud,et al. Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable , 2009, J. Comb. Theory, Ser. B.

[8] André Raspaud,et al. Planar graphs without cycles of length from 4 to 7 are 3-colorable , 2005, J. Comb. Theory, Ser. B.

[9] Ying-li Kang,et al. The 3-colorability of planar graphs without cycles of length 4, 6 and 9 , 2016, Discret. Math..