Decomposing Weighted Graphs
Combinatorics
2017-02-02 v1 Discrete Mathematics
Abstract
We solve the following problem: Can an undirected weighted graph G be parti- tioned into two non-empty induced subgraphs satisfying minimum constraints for the sum of edge weights at vertices of each subgraph? We show that this is possible for all constraints a(x), b(x) satisfying d_G(x) >= a(x) + b(x) + 2W_G(x), for every vertex x, where d_G(x), W_G(x) are, respectively, the sum and maximum of incident edge weights.
Keywords
Cite
@article{arxiv.1702.00205,
title = {Decomposing Weighted Graphs},
author = {Amir Ban},
journal= {arXiv preprint arXiv:1702.00205},
year = {2017}
}
Comments
To appear in Journal of Graph Theory