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Codiameters of 3-domination critical graphs with toughness more than one
- Source :
-
Discrete Mathematics . Mar2009, Vol. 309 Issue 5, p1067-1078. 12p. - Publication Year :
- 2009
-
Abstract
- Abstract: A graph is 3-domination-critical (3-critical, for short), if its domination number is 3 and the addition of any edge decreases by 1. In this paper, we show that every 3-critical graph with independence number 4 and minimum degree 3 is Hamilton-connected. Combining the result with those in [Y.J. Chen, F. Tian, B. Wei, Hamilton-connectivity of 3-domination critical graphs with , Discrete Mathematics 271 (2003) 1–12; Y.J. Chen, F. Tian, Y.Q. Zhang, Hamilton-connectivity of 3-domination critical graphs with , European Journal of Combinatorics 23 (2002) 777–784; Y.J. Chen, T.C.E. Cheng, C.T. Ng, Hamilton-connectivity of 3-domination critical graphs with , Discrete Mathematics 308 (2008) (in press)], we solve the following conjecture: a connected 3-critical graph is Hamilton-connected if and only if , where is the toughness of . [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 309
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 36771709
- Full Text :
- https://doi.org/10.1016/j.disc.2007.11.061