✦ LIBER ✦
Smallest (1, 2)-eulerian weight and shortest cycle covering
✍ Scribed by Cheng Zhao
- Book ID
- 102340018
- Publisher
- John Wiley and Sons
- Year
- 1994
- Tongue
- English
- Weight
- 358 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The concept of a (1, 2)‐eulerian weight was introduced and studied in several papers recently by Seymour, Alspach, Goddyn, and Zhang. In this paper, we proved that if G is a 2‐connected simple graph of order n (n ≧ 7) and w is a smallest (1, 2)‐eulerian weight of graph G, then |E~w=even~ | n ‐ 4, except for a family of graphs. Consequently, if G admits a nowhere‐zero 4‐flow and is of order at least 7, except for a family of graphs, the total length of a shortest cycle covering is at most | V(G) | + |E(G) |‐ 4. This result generalizes some previous results due to Bermond, Jackson, Jaeger, and Zhang.