Some Results on (1,2n – 1)-Odd Factors
Affiliation(s)
Department of Basic Course, Air Force Logistics College, Xuzhou, China. Aerial Four Station Department, Air Force Logistics College, Xuzhou, China.
Department of Basic Course, Air Force Logistics College, Xuzhou, China. Aerial Four Station Department, Air Force Logistics College, Xuzhou, China.
ABSTRACT
Let G be a graph. If there exists a spanning subgraph F such that dF(x) ∈ {1,3,…2n – 1}, then is called to be (1,2n – 1)-odd factor of G. Some sufficient and necessary conditions are given for G – U to have (1,2n – 1)-odd factor where U is any subset of V(G) such that |U| = k.
Let G be a graph. If there exists a spanning subgraph F such that dF(x) ∈ {1,3,…2n – 1}, then is called to be (1,2n – 1)-odd factor of G. Some sufficient and necessary conditions are given for G – U to have (1,2n – 1)-odd factor where U is any subset of V(G) such that |U| = k.
Cite this paper
M. Liu, Q. Yu, S. Wang and C. Huang, "Some Results on (1,2n – 1)-Odd Factors," Applied Mathematics, Vol. 3 No. 12, 2012, pp. 1874-1876. doi: 10.4236/am.2012.312255.
M. Liu, Q. Yu, S. Wang and C. Huang, "Some Results on (1,2n – 1)-Odd Factors," Applied Mathematics, Vol. 3 No. 12, 2012, pp. 1874-1876. doi: 10.4236/am.2012.312255.
References
[1] Y. Cui and M Cano, “Some Results on Odd Factors of Graphs,” Journal of Graph Theory, Vol. 12, No. 3, 1988, pp. 327-333. doi:10.1002/jgt.3190120305 [2] Z. Ryjá?ek, “On a Closure Concept in Claw-Free Graphs,” Journal of Combinatorial Theory, Series B, Vol. 70, No. 2, 1997, pp. 217-224. [3] O. Favaron, “On n-Factor-Critical Graphs,” Discussiones Mathematicae Graph Theory, Vol. 16, 1996, pp. 41-51. [4] N. Ananchuen and A. Daito, “Factor Criticality and Complete Closure of Graphs,” Discrete Mathematics, Vol. 265, No. 1-3, 2003, pp. 13-21. [5] G. Z. Liu and Q. L. Yu, “Toughness and Perfect Matchings in Graphs,” Ars combinatorial, Vol. 48, 1998, pp. 129-134. [6] C. P. Chen, “The Extendability of Matchings,” Journal of Beijing Agricultural Engineering University, Vol. 12, No. 4, 1992, pp. 36-39. [7] C. Teng, “Some New Results on (1,f)-Odd Factor of Graphs,” Journal of Shandong University, Vol. 31, No. 2, 1996, pp. 160-163. [8] C. Teng, “Some New Results on (1,f)-Odd Factor of Graphs,” Pure and Applied Mathematics, Vol. 10, 1994, pp. 188-192. [9] D. P. Sumner, “Graphs with 1-Factors,” Proceedings of the American Mathematical Society, Vol. 42, No. 1, 1974, pp. 8-12.
[1] Y. Cui and M Cano, “Some Results on Odd Factors of Graphs,” Journal of Graph Theory, Vol. 12, No. 3, 1988, pp. 327-333. doi:10.1002/jgt.3190120305 [2] Z. Ryjá?ek, “On a Closure Concept in Claw-Free Graphs,” Journal of Combinatorial Theory, Series B, Vol. 70, No. 2, 1997, pp. 217-224. [3] O. Favaron, “On n-Factor-Critical Graphs,” Discussiones Mathematicae Graph Theory, Vol. 16, 1996, pp. 41-51. [4] N. Ananchuen and A. Daito, “Factor Criticality and Complete Closure of Graphs,” Discrete Mathematics, Vol. 265, No. 1-3, 2003, pp. 13-21. [5] G. Z. Liu and Q. L. Yu, “Toughness and Perfect Matchings in Graphs,” Ars combinatorial, Vol. 48, 1998, pp. 129-134. [6] C. P. Chen, “The Extendability of Matchings,” Journal of Beijing Agricultural Engineering University, Vol. 12, No. 4, 1992, pp. 36-39. [7] C. Teng, “Some New Results on (1,f)-Odd Factor of Graphs,” Journal of Shandong University, Vol. 31, No. 2, 1996, pp. 160-163. [8] C. Teng, “Some New Results on (1,f)-Odd Factor of Graphs,” Pure and Applied Mathematics, Vol. 10, 1994, pp. 188-192. [9] D. P. Sumner, “Graphs with 1-Factors,” Proceedings of the American Mathematical Society, Vol. 42, No. 1, 1974, pp. 8-12.