Edge-Connectivity and Edges of Even Factors of Graphs

Discussiones Mathematicae Graph Theory

Kiani Dariush¹  Haghparast Nastaran¹ 

[1] Department of Mathematics and Computer Sciences,Amirkabir University of Technology, Tehran, Iran;

关键词: 3-edge-connected graph;    2-edge-connected graph;    even factor;    component;    05c70;    05c45;   

DOI  :  10.7151/dmgt.2082

来源: DOAJ

【 摘 要 】

An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Jackson and Yoshimoto showed that if G is a 3-edge-connected graph with |G| ≥ 5 and v is a vertex with degree 3, then G has an even factor F containing two given edges incident with v in which each component has order at least 5. We prove that this theorem is satisfied for each pair of adjacent edges. Also, we show that each 3-edge-connected graph has an even factor F containing two given edges e and f such that every component containing neither e nor f has order at least 5. But we construct infinitely many 3-edge-connected graphs that do not have an even factor F containing two arbitrary prescribed edges in which each component has order at least 5.

【 授权许可】

Unknown