Name
Abstract | ||
|---|---|---|
Let G be a 2-edge-connected undirected graph, A be an (additive) abelian group and A* = A−{0}. A graph G is A-connected if G has an orientation D(G) such that for every function b: V(G)↦A satisfying , there is a function f: E(G)↦A* such that for each vertex v∈V(G), the total amount of f values on the edges directed out from v minus the total amount of f values on the edges directed into v equals b(v). For a 2-edge-connected graph G, define Λg(G) = min{k: for any abelian group A with |A|⩾k, G is A-connected }. In this article, we prove the following Ramsey type results on group connectivity: Let G be a simple graph on n⩾6 vertices. If min{δ(G), δ(Gc)}⩾2, then either Λg(G)⩽4, or Λg(Gc)⩽4. Let Z3 denote the cyclic group of order 3, and G be a simple graph on n⩾44 vertices. If min{δ(G), δ(Gc)}⩾4, then either G is Z3-connected, or Gc is Z3-connected. © 2011 Wiley Periodicals, Inc. J Graph Theory © 2012 Wiley Periodicals, Inc. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1002/jgt.20595 | Journal of Graph Theory |
Keywords | Field | DocType |
abelian group,group connectivity,abelian group a,2-edge-connected undirected graph,wiley periodicals,cyclic group,complementary graphs,graph g,simple graph,2-edge-connected graph,total amount | Graph theory,Discrete mathematics,Graph,Abelian group,Combinatorics,Strongly regular graph,Bound graph,Vertex (geometry),Cyclic group,Mathematics | Journal |
Volume | Issue | Citations |
69 | 4 | 2 |
PageRank | References | Authors |
0.41 | 10 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xinmin Hou | 1 | 105 | 12.94 |
| Hong-Jian Lai | 2 | 631 | 97.39 |
| Ping Li | 3 | 21 | 7.14 |
| Cun-Quan Zhang | 4 | 496 | 69.81 |