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arXiv · 2007.12434

Partition of graphs with maximum degree ratio

Valentin Bouquet·François Delbot·Christophe Picouleau
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Abstract

Given 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 optimization or decision problems.

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Valentin Bouquet, François Delbot, Christophe Picouleau. 2020-07-24. Partition of graphs with maximum degree ratio. https://arxiv.org/abs/2007.12434

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