Partition of graphs with maximum degree ratio
V Bouquet, F Delbot, C Picouleau - arXiv preprint arXiv:2007.12434, 2020 - arxiv.org
V Bouquet, F Delbot, C Picouleau
arXiv preprint arXiv:2007.12434, 2020•arxiv.orgGiven a graph $ G $ and a non trivial partition $(V_1, V_2) $ of its vertex-set, the satisfaction
of a vertex $ v\in V_i $ is the ratio between the size of it's closed neighborhood in $ V_i $ and
the size of its closed neighborhood in $ G $. The worst ratio over all the vertices defines the
quality of the partition. We define $ q (G) $ the degree ratio of a graph as the maximum of the
worst ratio over all the non trivial partitions. We give bounds and exact values of $ q (G) $ for
some classes of graphs. We also show some complexity results for the associated …
of a vertex $ v\in V_i $ is the ratio between the size of it's closed neighborhood in $ V_i $ and
the size of its closed neighborhood in $ G $. The worst ratio over all the vertices defines the
quality of the partition. We define $ q (G) $ the degree ratio of a graph as the maximum of the
worst ratio over all the non trivial partitions. We give bounds and exact values of $ q (G) $ for
some classes of graphs. We also show some complexity results for the associated …
Given a graph and a non trivial partition of its vertex-set, the satisfaction of a vertex is the ratio between the size of it's closed neighborhood in and the size of its closed neighborhood in . The worst ratio over all the vertices defines the quality of the partition. We define the degree ratio of a graph as the maximum of the worst ratio over all the non trivial partitions. We give bounds and exact values of for some classes of graphs. We also show some complexity results for the associated optimization or decision problems.
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