Name
Abstract | ||
|---|---|---|
Esperet, de Joannis de Verclos, Le and Thomassé in [SIAM J. Discrete Math., 32(1) (2018), 534–542] introduced the problem that for an odd prime p, whether there exists an orientation D of a graph G for any mapping f:E(G)→Zp∗ and any Zp-boundary b of G, such that under D, at every vertex, the net out f-flow is the same as b(v) in Zp. Such an orientation D is called an (f,b;p)-orientation of G. Esperet et al. indicated that this problem is closely related to mod p-orientations of graphs, including Tutte’s nowhere zero 3-flow conjecture. Utilizing properties of additive bases and contractible configurations, we show that every graph G with Euler genus g and edge-connectivity κ′(G) admits an (f,b;p)-orientation for any mapping f:E(G)→Zp∗ and any Zp-boundary b of G, provided κ′(G)≥4p−6+⌊g∕2⌋if g≤2,(p−2)⌊6g+0.25+2.5⌋+1if g≥3,p4.98gif g is sufficiently large. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.ejc.2020.103163 | European Journal of Combinatorics |
DocType | Volume | ISSN |
Journal | 89 | 0195-6698 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jian-Bing Liu | 1 | 0 | 0.34 |
| Ping Li | 2 | 21 | 7.14 |
| Jiaao Li | 3 | 0 | 2.70 |
| Hong-Jian Lai | 4 | 631 | 97.39 |