| Title:
|
Even factor of bridgeless graphs containing two specified edges (English) |
| Author:
|
Haghparast, Nastaran |
| Author:
|
Kiani, Dariush |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
1105-1114 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Let $G$ be a bridgeless simple graph with minimum degree at least $3$. Jackson and Yoshimoto (2007) showed that $G$ has an even factor containing two arbitrary prescribed edges. They also proved that $G$ has an even factor in which each component has order at least four. Moreover, Xiong, Lu and Han (2009) showed that for each pair of edges $e_1$ and $e_2$ of $G$, there is an even factor containing $e_1$ and $e_2$ in which each component containing neither $e_1$ nor $e_2$ has order at least four. In this paper we improve this result and prove that $G$ has an even factor containing $e_1$ and $e_2$ such that each component has order at least four. (English) |
| Keyword:
|
bridgeless graph |
| Keyword:
|
components of an even factor |
| Keyword:
|
specified edge |
| MSC:
|
05C70 |
| idZBL:
|
Zbl 07031701 |
| idMR:
|
MR3881900 |
| DOI:
|
10.21136/CMJ.2018.0114-17 |
| . |
| Date available:
|
2018-12-07T06:23:27Z |
| Last updated:
|
2021-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147525 |
| . |
| Reference:
|
[1] Bondy, J. A., Murty, U. S. R.: Graph Theory with Applications.American Elsevier Publishing, New York (1976). Zbl 1226.05083, MR 0411988, 10.1007/978-1-349-03521-2 |
| Reference:
|
[2] Jackson, B., Yoshimoto, K.: Even subgraphs of bridgeless graphs and 2-factors of line graphs.Discrete Math. 307 (2007), 2775-2785. Zbl 1127.05080, MR 2362962, 10.1016/j.disc.2006.11.023 |
| Reference:
|
[3] Jackson, B., Yoshimoto, K.: Spanning even subgraphs of 3-edge-connected graphs.J. Graph Theory 62 (2009), 37-47. Zbl 1180.05057, MR 2547846, 10.1002/jgt.20386 |
| Reference:
|
[4] McKee, T. A.: Recharacterizing Eulerian: Intimations of new duality.Discrete Math. 51 (1984), 237-242. Zbl 0547.05043, MR 0762316, 10.1016/0012-365X(84)90004-9 |
| Reference:
|
[5] Xiong, L., Lu, M., Han, L.: The structure of even factors in claw-free graphs.Discrete Math. 309 (2009), 2417-2423. Zbl 1214.05139, MR 2509009, 10.1016/j.disc.2008.05.020 |
| . |
