On -choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles
Commentationes Mathematicae Universitatis Carolinae (2013)
- Volume: 54, Issue: 3, page 339-344
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topZhang, Haihui. "On $(4,1)^*$-choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles." Commentationes Mathematicae Universitatis Carolinae 54.3 (2013): 339-344. <http://eudml.org/doc/260657>.
@article{Zhang2013,
abstract = {A graph $G$ is called $(k,d)^*$-choosable if for every list assignment $L$ satisfying $|L(v)|= k$ for all $v\in V(G)$, there is an $L$-coloring of $G$ such that each vertex of $G$ has at most $d$ neighbors colored with the same color as itself. In this paper, it is proved that every toroidal graph without chordal 7-cycles and adjacent 4-cycles is $(4,1)^*$-choosable.},
author = {Zhang, Haihui},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {toroidal graph; defective choosability; chord; toroidal graph; defective choosability; chord},
language = {eng},
number = {3},
pages = {339-344},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $(4,1)^*$-choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles},
url = {http://eudml.org/doc/260657},
volume = {54},
year = {2013},
}
TY - JOUR
AU - Zhang, Haihui
TI - On $(4,1)^*$-choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 3
SP - 339
EP - 344
AB - A graph $G$ is called $(k,d)^*$-choosable if for every list assignment $L$ satisfying $|L(v)|= k$ for all $v\in V(G)$, there is an $L$-coloring of $G$ such that each vertex of $G$ has at most $d$ neighbors colored with the same color as itself. In this paper, it is proved that every toroidal graph without chordal 7-cycles and adjacent 4-cycles is $(4,1)^*$-choosable.
LA - eng
KW - toroidal graph; defective choosability; chord; toroidal graph; defective choosability; chord
UR - http://eudml.org/doc/260657
ER -
References
top- Chen Y., Zhu W., Wang W., 10.1016/j.camwa.2008.03.036, Comput. Math. Appl. 56 (2008), 2073–2078. Zbl1165.05342MR2466712DOI10.1016/j.camwa.2008.03.036
- Cushing W., Kierstead H.A., 10.1016/j.ejc.2009.11.013, European J. Combin. 31 (2009), 1385–1397. Zbl1221.05077MR2644426DOI10.1016/j.ejc.2009.11.013
- Eaton N., Hull T., Defective list colorings of planar graphs, Bull. Inst. Comb. Appl. 25 (1999), 79–87. Zbl0916.05026MR1668108
- Lih K., Song Z., Wang W., Zhang K., 10.1016/S0893-9659(00)00147-6, Appl. Math. Lett. 14 (2001), 269–273. Zbl0978.05029MR1820611DOI10.1016/S0893-9659(00)00147-6
- Škrekovski R., 10.1017/S0963548399003752, Comb. Prob. Comp. 8 (1999), 293–299. Zbl0940.05027MR1702609DOI10.1017/S0963548399003752
- Škrekovski R., 10.1017/S096354839900396X, Comb. Prob. Comp. 8 (1999), 493–507. MR1731984DOI10.1017/S096354839900396X
- Škrekovski R., 10.1016/S0012-365X(99)00145-4, Discrete Math. 214 (2000), 221–233. Zbl0940.05027MR1743637DOI10.1016/S0012-365X(99)00145-4
- Dong W., Xu B., 10.1016/j.dam.2008.06.023, Discrete Appl. Math. 28 (2009), 433–436. Zbl1209.05076MR2479819DOI10.1016/j.dam.2008.06.023
- Xu B., Zhang H., 10.1016/j.dam.2006.04.042, Discrete Appl. Math. 155 (2007), 74–78. Zbl1107.05039MR2281358DOI10.1016/j.dam.2006.04.042
- Zhang L., 10.1016/j.dam.2011.10.019, Discrete Appl. Math. 160 (2012), 332–338. Zbl1241.05037MR2862339DOI10.1016/j.dam.2011.10.019
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.