BibTex RIS Cite

SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI

Year 2016, Volume: 4 Issue: 2, 91 - 98, 25.08.2016

Ummahan Akcan Emrah Akyar Handan Akyar

https://doi.org/10.20290/btdb.53177

Abstract

Bu çalışmada, n>=1 ve k>=2 iken S(n,k) Sierpinski çizgelerinin oyun renk sayısı ve özel olarak k=3 için S(n,k) Sierpinski çizgelerinin oyun kromatik sayısı hesaplanmıştır. Ayrıca Sierpinski çizgeler ile ilgili bazı açık problemlerden de bahsedilmiştir.

Keywords

Sierpinski çizge Oyun kromatik sayısı Oyun renk sayısı

References

  • Bodlaender H L. On the complexity of some coloring games. International Journal of Foundations of Computer Science 1991; 2: 133-147.
  • Dinski T, Zhu X. A bound for the game chromatic number of graphs. Discrete Mathematics 1999; : 109-115.
  • Faigle U, Kern U, Kierstead H A, Trotter W T. On the game chromatic number of some classes of graphs. Ars Combinatoria 1993; 35: 143-150.
  • Gardner M. Mathematical Games. Scientific American 1981; 23.
  • Guan D J, Zhu X. Game chromatic number of outerplanar graphs. Journal of Graph Theory 1999; : 67-70.
  • Hinz A M, Parisse D. Coloring Hanoi and Sierpinski graphs. Discrete Mathematics 2012; 312: 1521
  • Jakovac M, Klavžar S. Vertex-, edge-, and total-colorings of Sierpinski-like graphs. Discrete Mathematics 2009; 309: 1548-1556.
  • Kierstead H A., Trotter W T. Planar graph coloring with an uncooperative partner. Journal of Graph Theory 1994; 18: 569-584.
  • Kierstead H A. A simple competitive graph coloring algorithm. Journal of Combinatorial Theory Series B 2000; 78: 57-68.
  • Kierstead H A., Yang D. Very asymmetric marking games. Order 2005; 22: 93-107.
  • Klavžar S, Milutinović U. Graphs S(n, k) and a variant of the Tower of Hanoi problem. Czechoslovak Mathematical Journal 1997; 47: 95-104.
  • Klavžar S. Coloring Sierpinski graphs and Sierpinski gasket graphs. Taiwanese Journal of Mathematics 2008; 12: 513-522.
  • Parisse D. On some metric properties of the Sierpinski graphs S(n, k). Ars Combinatoria 2009; 90: 160.
  • Paul D, Rajasingh I. Acyclic edge-coloring of Sierpinski-like graphs. International Journal of Pure and Applied Mathematics 2013; 87: 855-862.
  • Raspaud A, Wu J. Game chromatic number of toroidal grids. Information Processing Letters 2009; : 1183-1186.
  • Sidorowicz E. The game chromatic number and the game colouring number of cactuses. Information Processing Letters 2007; 102: 147-151.
  • Wu J, Zhu X. Lower bounds for the game colouring number of partial -trees and planar graphs Discrete Mathematics 2008; 308: 2637-2642.
  • Zhu X. The game coloring number of planar graphs Journal of Combinatorial Theory Series B ; 75: 245-258. Zhu X. Refined activation strategy for the marking game. Journal of Combinatorial Theory Series B 2008; 98: 1-18.

Year 2016, Volume: 4 Issue: 2, 91 - 98, 25.08.2016

Ummahan Akcan Emrah Akyar Handan Akyar

https://doi.org/10.20290/btdb.53177

Abstract

References

  • Bodlaender H L. On the complexity of some coloring games. International Journal of Foundations of Computer Science 1991; 2: 133-147.
  • Dinski T, Zhu X. A bound for the game chromatic number of graphs. Discrete Mathematics 1999; : 109-115.
  • Faigle U, Kern U, Kierstead H A, Trotter W T. On the game chromatic number of some classes of graphs. Ars Combinatoria 1993; 35: 143-150.
  • Gardner M. Mathematical Games. Scientific American 1981; 23.
  • Guan D J, Zhu X. Game chromatic number of outerplanar graphs. Journal of Graph Theory 1999; : 67-70.
  • Hinz A M, Parisse D. Coloring Hanoi and Sierpinski graphs. Discrete Mathematics 2012; 312: 1521
  • Jakovac M, Klavžar S. Vertex-, edge-, and total-colorings of Sierpinski-like graphs. Discrete Mathematics 2009; 309: 1548-1556.
  • Kierstead H A., Trotter W T. Planar graph coloring with an uncooperative partner. Journal of Graph Theory 1994; 18: 569-584.
  • Kierstead H A. A simple competitive graph coloring algorithm. Journal of Combinatorial Theory Series B 2000; 78: 57-68.
  • Kierstead H A., Yang D. Very asymmetric marking games. Order 2005; 22: 93-107.
  • Klavžar S, Milutinović U. Graphs S(n, k) and a variant of the Tower of Hanoi problem. Czechoslovak Mathematical Journal 1997; 47: 95-104.
  • Klavžar S. Coloring Sierpinski graphs and Sierpinski gasket graphs. Taiwanese Journal of Mathematics 2008; 12: 513-522.
  • Parisse D. On some metric properties of the Sierpinski graphs S(n, k). Ars Combinatoria 2009; 90: 160.
  • Paul D, Rajasingh I. Acyclic edge-coloring of Sierpinski-like graphs. International Journal of Pure and Applied Mathematics 2013; 87: 855-862.
  • Raspaud A, Wu J. Game chromatic number of toroidal grids. Information Processing Letters 2009; : 1183-1186.
  • Sidorowicz E. The game chromatic number and the game colouring number of cactuses. Information Processing Letters 2007; 102: 147-151.
  • Wu J, Zhu X. Lower bounds for the game colouring number of partial -trees and planar graphs Discrete Mathematics 2008; 308: 2637-2642.
  • Zhu X. The game coloring number of planar graphs Journal of Combinatorial Theory Series B ; 75: 245-258. Zhu X. Refined activation strategy for the marking game. Journal of Combinatorial Theory Series B 2008; 98: 1-18.
There are 18 citations in total.

Details

Journal Section Articles
Authors

Ummahan Akcan This is me

Emrah Akyar

Handan Akyar

Publication Date August 25, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Akcan, U., Akyar, E., & Akyar, H. (2016). SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI. Anadolu University Journal of Science and Technology B - Theoretical Sciences, 4(2), 91-98. https://doi.org/10.20290/btdb.53177
AMA Akcan U, Akyar E, Akyar H. SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI. AUBTD-B. October 2016;4(2):91-98. doi:10.20290/btdb.53177
Chicago Akcan, Ummahan, Emrah Akyar, and Handan Akyar. “SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 4, no. 2 (October 2016): 91-98. https://doi.org/10.20290/btdb.53177.
EndNote Akcan U, Akyar E, Akyar H (October 1, 2016) SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI. Anadolu University Journal of Science and Technology B - Theoretical Sciences 4 2 91–98.
IEEE U. Akcan, E. Akyar, and H. Akyar, “SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI”, AUBTD-B, vol. 4, no. 2, pp. 91–98, 2016, doi: 10.20290/btdb.53177.
ISNAD Akcan, Ummahan et al. “SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 4/2 (October 2016), 91-98. https://doi.org/10.20290/btdb.53177.
JAMA Akcan U, Akyar E, Akyar H. SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI. AUBTD-B. 2016;4:91–98.
MLA Akcan, Ummahan et al. “SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI”. Anadolu University Journal of Science and Technology B - Theoretical Sciences, vol. 4, no. 2, 2016, pp. 91-98, doi:10.20290/btdb.53177.
Vancouver Akcan U, Akyar E, Akyar H. SIERPINSKI ÇİZGELERİN OYUN KROMATİK VE OYUN RENK SAYILARI. AUBTD-B. 2016;4(2):91-8.
 Download Cover Image