Even factor of bridgeless graphs containing two specified edges
Nastaran Haghparast; Dariush Kiani
Czechoslovak Mathematical Journal (2018)
- Volume: 68, Issue: 4, page 1105-1114
- ISSN: 0011-4642
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topHaghparast, Nastaran, and Kiani, Dariush. "Even factor of bridgeless graphs containing two specified edges." Czechoslovak Mathematical Journal 68.4 (2018): 1105-1114. <http://eudml.org/doc/294209>.
@article{Haghparast2018,
abstract = {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.},
author = {Haghparast, Nastaran, Kiani, Dariush},
journal = {Czechoslovak Mathematical Journal},
keywords = {bridgeless graph; components of an even factor; specified edge},
language = {eng},
number = {4},
pages = {1105-1114},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Even factor of bridgeless graphs containing two specified edges},
url = {http://eudml.org/doc/294209},
volume = {68},
year = {2018},
}
TY - JOUR
AU - Haghparast, Nastaran
AU - Kiani, Dariush
TI - Even factor of bridgeless graphs containing two specified edges
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 4
SP - 1105
EP - 1114
AB - 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.
LA - eng
KW - bridgeless graph; components of an even factor; specified edge
UR - http://eudml.org/doc/294209
ER -
References
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- Jackson, B., Yoshimoto, K., 10.1016/j.disc.2006.11.023, Discrete Math. 307 (2007), 2775-2785. (2007) Zbl1127.05080MR2362962DOI10.1016/j.disc.2006.11.023
- Jackson, B., Yoshimoto, K., 10.1002/jgt.20386, J. Graph Theory 62 (2009), 37-47. (2009) Zbl1180.05057MR2547846DOI10.1002/jgt.20386
- McKee, T. A., 10.1016/0012-365X(84)90004-9, Discrete Math. 51 (1984), 237-242. (1984) Zbl0547.05043MR0762316DOI10.1016/0012-365X(84)90004-9
- Xiong, L., Lu, M., Han, L., 10.1016/j.disc.2008.05.020, Discrete Math. 309 (2009), 2417-2423. (2009) Zbl1214.05139MR2509009DOI10.1016/j.disc.2008.05.020
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