Article
| Title: | Partitioning a planar graph without chordal 5-cycles into two forests (English) |
| Author: | Wang, Yang |
| Author: | Wang, Weifan |
| Author: | Kong, Jiangxu |
| Author: | Wang, Yiqiao |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 377-388 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | It was known that the vertex set of every planar graph can be partitioned into three forests. We prove that the vertex set of a planar graph without chordal 5-cycles can be partitioned into two forests. This extends a result obtained by Raspaud and Wang in 2008. (English) |
| Keyword: | planar graph |
| Keyword: | vertex-arboricity |
| Keyword: | forest |
| Keyword: | vertex partition |
| MSC: | 05C15 |
| DOI: | 10.21136/CMJ.2024.0065-23 |
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| Date available: | 2024-07-10T14:49:42Z |
| Last updated: | 2024-07-15 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152446 |
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| Reference: | [1] Borodin, O. V., Ivanova, A. O.: Planar graphs without 4-cycles adjacent to 3-cycles are list vertex 2-arborable.J. Graph Theory 62 (2009), 234-240. Zbl 1180.05035, MR 2566928, 10.1002/jgt.20394 |
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| Reference: | [4] Chen, M., Raspaud, A., Wang, W.: Vertex-arboricity of planar graphs without intersecting triangles.Eur. J. Comb. 33 (2012), 905-923. Zbl 1250.05062, MR 2889524, 10.1016/j.ejc.2011.09.017 |
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| Reference: | [7] Huang, D., Shiu, W. C., Wang, W.: On the vertex-arboricity of planar graphs without 7-cycles.Discrete Math. 312 (2012), 2304-2315. Zbl 1245.05029, MR 2926103, 10.1016/j.disc.2012.03.035 |
| Reference: | [8] Huang, D., Wang, W.: Vertex arboricity of planar graphs without chordal 6-cycles.Int. J. Comput. Math. 90 (2013), 258-272. Zbl 1278.05100, MR 3016834, 10.1080/00207160.2012.727989 |
| Reference: | [9] Raspaud, A., Wang, W.: On the vertex-arboricity of planar graphs.Eur. J. Comb. 29 (2008), 1064-1075. Zbl 1144.05024, MR 2408378, 10.1016/j.ejc.2007.11.022 |
| Reference: | [10] Stein, S. K.: $B$-sets and planar maps.Pac. J. Math. 37 (1971), 217-224. Zbl 0194.56101, MR 0306053, 10.2140/pjm.1971.37.217 |
| Reference: | [11] Wang, Y., Wang, Y., Lih, K.-W.: Partitioning kite-free planar graphs into two forests.J. Graph Theory 106 (2024), 30-56. Zbl 7823339, MR 4730107, 10.1002/jgt.23062 |
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