J4 ›› 2009, Vol. 44 ›› Issue (8): 13-15.

• Articles • Previous Articles     Next Articles

Degree conditions for bipartite graphs to contain 6-cycles

  

  1. ZOU Qing-song,LI Shuo: School of Mathematics, Shandong University, Jinan 250100, Shandong, China;
    LI Shuo,YNAG Xing-gang: Department of Mathematics, Changji University, Changji 831100, Xinjiang, China
  • Received:2009-01-03 Online:2009-08-16 Published:2009-11-08

Abstract:

Let G=(V1,V2;E) be a balanced bipartite  graph with |V1|=|V2|=3k and k≥1. If the minimum degree δ≥2k,  then G either contains k  vertices d isjoint 6-cycles or contains k-1 vertices disjoint 6-cycles and a 4-cycle.

Key words: bipartite graphs; 6-cycle; degree conditions

CLC Number: 

  • O157.5
[1] . On the Smarandachelyadjacentvertex edge coloring of some double graphs [J]. J4, 2009, 44(12): 25-29.
[2] DONG Ai-Jun, LI Guo-Jun, JU Jing-Song. List edge and list total colorings of planar graphs with adjacent triangles [J]. J4, 2009, 44(10): 17-20.
[3] WANG Chao. A degree condition for graphs to have Hamiltonian (g,f)-factors [J]. J4, 2009, 44(10): 21-25.
[4] LIU Shen-Sheng, SHU Zhi-Jiang. An upper bound on the vertex distinguishing IE total chromatic number of graphs [J]. J4, 2009, 44(10): 14-16.
[5] GAO Yu-Fen, WEI Xiao-Li. On the extremal Merrifield-Simmons index with  respect to trees having given number of endvertices [J]. J4, 2009, 44(8): 16-20.
[6] YUAN Xiu-Hua. Signed edge total domination numbers of graphs [J]. J4, 2009, 44(8): 21-24.
[7] LIU Hai-Yang, MA Cheng-Gang, WANG Zhi-Beng. Graham's conjecture on the product of the thorn graph [J]. J4, 2009, 44(8): 25-30.
[8] DUAN Ci-Meng, LV Ping-Li, MIAO Lian-Yang, MIAO Zheng-Ke. L(2,1,1)-Labeling of simple graphs [J]. J4, 2009, 44(8): 31-34.
[9] LIU Xiao-Yan. null [J]. J4, 2008, 43(12): 28-30.
[10] GENG Jian-yan,YAN Jin,LI Feng . Vertex-disjoint 4-cycle in a bipartite graph [J]. J4, 2008, 43(5): 87-92 .
[11] PAN Rui-xia,LAN Mei,LIU Gui-zhen . A condition of isolated toughness on the existence of fractional [a,b]-factors of graphs [J]. J4, 2008, 43(5): 93-96 .
[12] 林丽美1,2,周书明1,2,许力1,2. t/t-diagnosability and diagnosis algorithm on hierarchical cubic network [J]. J4, 2013, 48(7): 85-92.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!