ArticleOriginal scientific text

Title

Edge maximal C2k+1-edge disjoint free graphs

Authors 1, 2

Affiliations

  1. Department of Mathematics, Yarmouk University, Irbid-Jordan
  2. Yarmouk University, Department of Mathematics, Irbid-Jordan, Department of Mathematics, Physics and Statistics, Qatar University, Doha-Qatar

Abstract

For two positive integers r and s, (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{(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 (n;r,2k+1).

Keywords

extremal graphs, edge disjoint, cycles

Bibliography

  1. M.S. Bataineh, Some Extremal Problems in Graph Theory, Ph.D Thesis, Curtin University of Technology (Australia, 2007).
  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.
  3. J. Bondy, Large cycle in graphs, Discrete Math. 1 (1971) 121-132, doi: 10.1016/0012-365X(71)90019-7.
  4. J. Bondy, Pancyclic graphs, J. Combin. Theory (B) 11 (1971) 80-84, doi: 10.1016/0095-8956(71)90016-5.
  5. J. Bondy and U. Murty, Graph Theory with Applications (The MacMillan Press, London, 1976).
  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.
  7. L. Caccetta, A problem in extremal graph theory, Ars Combin. 2 (1976) 33-56.
  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).
  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.
  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.
  11. R. Jia, Some Extremal Problems in Graph Theory, Ph.D Thesis, Curtin University of Technology (Australia, 1998).
  12. P. Turán, On a problem in graph theory, Mat. Fiz. Lapok 48 (1941) 436-452.
Pages:
271-278
Main language of publication
English
Received
2010-08-27
Accepted
2011-03-15
Published
2012
Exact and natural sciences