Mod (2p+1)-orientations in line graphs

  • Authors:

  • Hong-Jian Lai;Hao Li;Ping Li;Yanting Liang;Senmei Yao

  • Affiliations:

  • College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China and Department of Mathematics, West Virginia University, Morgantown, WV 26506, United States;Department of Mathematics, Renmin University of China, Beijing 100872, China;Department of Mathematics, West Virginia University, Morgantown, WV 26506, United States;Department of Mathematics, West Virginia University, Morgantown, WV 26506, United States and Mathematics and Computer Science Department, St. Marys College of Maryland, St. Marys City, MD 20686, U ...;Department of Mathematics, West Virginia University, Morgantown, WV 26506, United States

  • Venue:
  • Information Processing Letters
  • Year:
  • 2011

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Abstract

Jaeger in 1984 conjectured that every (4p)-edge-connected graph has a mod (2p+1)-orientation. It has also been conjectured that every (4p+1)-edge-connected graph is mod (2p+1)-contractible. In [Z.-H. Chen, H.-J. Lai, H. Lai, Nowhere zero flows in line graphs, Discrete Math. 230 (2001) 133-141], it has been proved that if G has a nowhere-zero 3-flow and the minimum degree of G is at least 4, then L(G) also has a nowhere-zero 3-flow. In this paper, we prove that the above conjectures on line graphs would imply the truth of the conjectures in general, and we also prove that if G has a mod (2p+1)-orientation and @d(G)=4p, then L(G) also has a mod (2p+1)-orientation, which extends a result in Chen et al. (2001) [2].