A graph G is perfect if for every induced subgraph H of G the chromatic number x(H) equals the largest number w ( H ) of pairwise adjacent vertices in H. Berge's famous Strong Perfect Graph Conjecture asserts that a graph G is perfect if and only if neither G nor its complement C contains an odd cho
On the strong circular 5-flow conjecture
✍ Scribed by Edita Máčajová; André Raspaud
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 163 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The Strong Circular 5‐flow Conjecture of Mohar claims that each snark—with the sole exception of the Petersen graph—has circular flow number smaller than 5. We disprove this conjecture by constructing an infinite family of cyclically 4‐edge connected snarks whose circular flow number equals 5. © 2006 Wiley Periodicals, Inc. J Graph Theory
📜 SIMILAR VOLUMES
Heawood proved that every planar graph with no 1-cycles is vertex 5colorable, which is equivalent to the statement that every planar graph with no 1-bonds has a nowhere-zero 5-flow. Tutte has conjectured that every graph with no 1-bonds has a nowhere-zero 5-flow. We show that Tutte's 5-Flow Conjectu