For two positive integers r and s, 𝓖(n;r,s) denotes to the class of graphs on n vertices containing no r of s-edge disjoint cycles and f(n;r,s) = max{𝓔(G):G ∈ 𝓖(n;r,s)}. In this paper, for integers r ≥ 2 and k ≥ 1, we determine f(n;r,2k+1) and characterize the edge maximal members in 𝓖(n;r,2k+1).
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1601,
author = {M.S.A. Bataineh and M.M.M. Jaradat},
title = {Edge maximal $C\_{2k+1}$-edge disjoint free graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {32},
year = {2012},
pages = {271-278},
zbl = {1255.05107},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1601}
}
M.S.A. Bataineh; M.M.M. Jaradat. Edge maximal $C_{2k+1}$-edge disjoint free graphs. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 271-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1601/
[000] [1] M.S. Bataineh, Some Extremal Problems in Graph Theory, Ph.D Thesis, Curtin University of Technology (Australia, 2007).
[001] [2] M.S. Bataineh and M.M.M. Jaradat, Edge maximal C₃ and C₅-edge disjoint free graphs, International J. Math. Combin. 1 (2011) 82-87. | Zbl 1230.05171
[002] [3] J. Bondy, Large cycle in graphs, Discrete Math. 1 (1971) 121-132, doi: 10.1016/0012-365X(71)90019-7. | Zbl 0224.05120
[003] [4] J. Bondy, Pancyclic graphs, J. Combin. Theory (B) 11 (1971) 80-84, doi: 10.1016/0095-8956(71)90016-5. | Zbl 0183.52301
[004] [5] J. Bondy and U. Murty, Graph Theory with Applications (The MacMillan Press, London, 1976). | Zbl 1226.05083
[005] [6] S. Brandt, A sufficient condition for all short cycles, Discrete Appl. Math. 79 (1997) 63-66, doi: 10.1016/S0166-218X(97)00032-2. | Zbl 0882.05081
[006] [7] L. Caccetta, A problem in extremal graph theory, Ars Combin. 2 (1976) 33-56. | Zbl 0349.05119
[007] [8] L. Caccetta and R. Jia, Edge maximal non-bipartite Hamiltonian graphs without cycles of length 5, Technical Report.14/97. School of Mathematics and Statistics, Curtin University of Technology (Australia, 1997).
[008] [9] L. Caccetta and R. Jia, Edge maximal non-bipartite graphs without odd cycles of prescribed length, Graphs and Combin. 18 (2002) 75-92, doi: 10.1007/s003730200004. | Zbl 0997.05050
[009] [10] Z. Füredi, On the number of edges of quadrilateral-free graphs, J. Combin. Theory (B) 68 (1996) 1-6, doi: 10.1006/jctb.1996.0052. | Zbl 0858.05063
[010] [11] R. Jia, Some Extremal Problems in Graph Theory, Ph.D Thesis, Curtin University of Technology (Australia, 1998).
[011] [12] P. Turán, On a problem in graph theory, Mat. Fiz. Lapok 48 (1941) 436-452.