Name
Abstract | ||
|---|---|---|
We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory Part of this research was conducted at Cornell University, Ithaca, New York 14853-4201. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1002/jgt.v51:1 | Journal of Graph Theory |
Keywords | Field | DocType |
balance,wheel graph,data structure,cyclic group,discrete mathematics,abelian group | Discrete mathematics,Combinatorics,Gain graph,Robertson–Seymour theorem,Forbidden graph characterization,Partial k-tree,Graph product,Pathwidth,1-planar graph,Cycle graph (algebra),Mathematics | Journal |
Volume | Issue | ISSN |
51 | 1 | J. Graph Theory, 51 (2006), no. 1, 1--21. |
Citations | PageRank | References |
1 | 0.40 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Konstantin Rybnikov | 1 | 7 | 1.71 |
| T. Zaslavsky | 2 | 297 | 56.67 |