Spanning Eulerian Subgraphs of 2-Edge-Connected Graphs

详细信息    查看全文

• 作者：Xiangwen Li (1)
  Chunxiang Wang (1)
  Qiong Fan (1)
  Zhaohong Niu (2)
  Liming Xiong (3) (4)
  
• 关键词：Supereulerian ; Collapsible ; Eulerian graphs
• 刊名：Graphs and Combinatorics
• 出版年：2013
• 出版时间：March 2013
• 年：2013
• 卷：29
• 期：2
• 页码：275-280
• 全文大小：167KB
• 参考文献：1. Bondy J.A., Murty U.S.R.: Graph Theory with Applications. American Elsevier, New York (1976)
  2. Broersma H.J., Xiong L.: A note on minimun degree conditions for supereulerian graphs. Discrete Appl. Math. g class="a-plus-plus">120g>, 35-3 (2002) g/10.1016/S0166-218X(01)00278-5">CrossRef
  3. Catlin P.A.: A reduction method to find spanning eulerian subgraphs. J. Graph Theory g class="a-plus-plus">12g>, 29-5 (1998) g/10.1002/jgt.3190120105">CrossRef
  4. Catlin P.A., Han Z.Y., Lai H.-J.: Graphs without spanning closed trails. Discrete Math. g class="a-plus-plus">160g>, 81-1 (1996) g/10.1016/S0012-365X(95)00149-Q">CrossRef
  5. Catlin P.A., Li X.: Supereulerian graphs of minimum degree at least 4. J. Adv. Math. g class="a-plus-plus">160g>, 65-9 (1999)
  6. Jaeger F.: A note on sub-Eulerian graphs. J. Graph Theory g class="a-plus-plus">3g>, 91-3 (1979) g/10.1002/jgt.3190030110">CrossRef
  7. Lai H.-J., Liang Y.: Supereulerian graphs in the graph family / C ₂(6, / k). Discrete Appl. Math. g class="a-plus-plus">159g>, 467-77 (2011) g/10.1016/j.dam.2010.12.005">CrossRef
  8. Li D., Lai H.-J., Zhan M.: Eulerian subgraphs and Hamilton-connected line graphs. Discrete Appl. Math. g class="a-plus-plus">145g>, 422-28 (2005) g/10.1016/j.dam.2004.04.005">CrossRef
  9. Li X., Li D., Lai H.-J.: The supereulerian graphs in the graph family / C( / l, / k). Discrete Math. g class="a-plus-plus">309g>, 2937-942 (2009) g/10.1016/j.disc.2008.06.038">CrossRef
  
• 作者单位：Xiangwen Li (1)
  Chunxiang Wang (1)
  Qiong Fan (1)
  Zhaohong Niu (2)
  Liming Xiong (3) (4)
  
  1. Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China
  2. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China
  3. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China
  4. Department of Mathematics, Jiangxi Normal University, Nanchang, 330027, China
  
• ISSN：1435-5914

文摘

For integers l and k with l >?0 and k >?0, let ${{\fancyscript{C}}(l, k)}$ denote the family of 2-edge-connected graphs G such that for each bond cut |S|??3, each component of G ?S has at least (|V(G)| ?k)/l vertices. In this paper we prove that if ${G\in {\fancyscript{C}}(7, 0)}$ , then G is not supereulerian if and only if G can be contracted to one of the nine specified graphs. Our result extends some earlier results (Catlin and Li in J Adv Math 160:65-9, 1999; Broersma and Xiong in Discrete Appl Math 120:35-3, 2002; Li et?al. in Discrete Appl Math 145:422-28, 2005; Li et?al. in Discrete Math 309:2937-942, 2009; Lai and Liang in Discrete Appl Math 159:467-77, 2011).