Cycle and Circle Tests of Balance in Gain Graphs: Forbidden Minors and Their Groups

Details Cycle and Circle Tests of Balance in Gain Graphs: Forbidden Minors and Their Groups Cycle and Circle Tests of Balance in Gain Graphs: Forbidden Minors and Their Groups

2002-09-24

arxiv.org/abs/math/0209316v3

J. Graph Theory, 51 (2006), no. 1, 1--21.

Mathematics

Combinatorics

19 pages, 3 figures. Format: Latex2e. Changes: minor. To appear in Journal of Graph Theory

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Cycle and Circle Tests of Balance in Gain Graphs: Forbidden Minors and Their Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cycle and Circle Tests of Balance in Gain Graphs: Forbidden Minors and Their Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cycle and Circle Tests of Balance in Gain Graphs: Forbidden Minors and Their Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-612593