Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (κ²½λΆλŒ€ν•™κ΅ μžμ—°κ³Όν•™λŒ€ν•™ μˆ˜ν•™κ³Ό)
ꢌ호 ν‘œμ§€
DOI QRμ½”λ“œ

DOI QR Code

Edge-Maximal πœƒk+1-Edge Disjoint Free Graphs

  • Jaradat, Mohammed M.M. (Department of Mathematics, Statistics and Physics, Qatar University) ;
  • Bataineh, Mohammed S.A. (Department of Mathematics, Yarmouk University)
  • Received : 2010.09.25
  • Accepted : 2012.11.07
  • Published : 2014.03.23
Download PDF
⟨ Previous Next ⟩

Abstract

For two positive integers r and s, $\mathcal{G}$(n; r; ${\theta}_s$) denotes to the class of graphs on n vertices containing no r of edge disjoint ${\theta}_s$-graphs and f(n; r; ${\theta}_s$) = max{${\varepsilon}(G)$ : G ${\in}$ $\mathcal{G}$(n; r; ${\theta}_s$)}. In this paper, for integers r, $k{\geq}2$, we determine f(n; r; ${\theta}_{2k+1}$) and characterize the edge maximal members in G(n; r; ${\theta}_{2k+1}$).

Keywords

References

  1. M. Bataineh, Some Extermal problems in graph theory, Ph.D Thesis, Curtin University of Technology, Australia, (2007).
  2. M. Bataineh and M. M. Jaradat, Edge Maximal $C_{2k+1}$-edge disjoint free graphs, Discussiones Mathematicae Graph Theory, 32(2012), 269-276.
  3. M. Bataineh, M. M. Jaradat and E. Al-Shboul, Edge-maximal graphs without ${\theta}_5$-graphs, Accepted in Ars Combinatoria.
  4. J. Bondy, Large cycle in graphs, Discrete Mathematics, 1(1971a), 121-132. https://doi.org/10.1016/0012-365X(71)90019-7
  5. J. Bondy, Pancyclic Graphs, J. Combinatorial Theory Ser. B, 11(1971b), 80-84. https://doi.org/10.1016/0095-8956(71)90016-5
  6. J. Bondy and U. Murty, Graph Theory with Applications, The MacMillan Press, London, (1976).
  7. S. Brandt, A sufficient condition for all short cycles, Discrete Applied Mathematics, 79(1997), 63-66. https://doi.org/10.1016/S0166-218X(97)00032-2
  8. L. Caccetta, A problem in extremal graph theory, ARS Combinatoria, 2(1976), 33-56.
  9. L. Caccetta and R. Jia, Edge maximal non-bipartite graphs without odd cycles of prescribed length, Graphs and Combinatorics, 18(2002), 75-92. https://doi.org/10.1007/s003730200004
  10. M. M. Jaradat, M. Bataineh and E. Al-Shboul, Edge-maximal graphs without ${\theta}_{2k+1}$-graphs, Accepted in AKCE International Journal of Graphs and Combinatorics.
  11. R. Jia, Some Extremal problems in graph theory, Ph.D Thesis, Curtin University of Technology, Australia, (1998).