Name
Abstract | ||
|---|---|---|
Let V(D)=X∪Y be a bipartition of a directed graph D. We use e(X,Y) to denote the number of arcs in D from X to Y. Motivated by a conjecture posed by Lee, Loh and Sudakov (2016) [16], we study bipartitions of oriented graphs. Let D be an oriented graph with m arcs. In this paper, it is proved that if the minimum degree of D is δ, then D admits a bipartition V(D)=V1∪V2 such that min{e(V1,V2),e(V2,V1)}≥(δ−14δ+o(1))m. Moreover, if the minimum semidegree d=min{δ+(D),δ−(D)} of D is at least 21, then D admits a bipartition V(D)=V1∪V2 such that min{e(V1,V2),e(V2,V1)}≥(d2(2d+1)+o(1))m. Both bounds are asymptotically best possible. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.jctb.2018.03.003 | Journal of Combinatorial Theory, Series B |
Keywords | Field | DocType |
Oriented graph,Partition,Semidegree,Tight component | Graph,Combinatorics,Directed graph,Conjecture,Physics | Journal |
Volume | ISSN | Citations |
132 | 0095-8956 | 1 |
PageRank | References | Authors |
0.36 | 15 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jianfeng Hou | 1 | 10 | 2.65 |
| Shu-Fei Wu | 2 | 9 | 2.92 |