Partition of graphs with maximum degree ratio

Valentin Bouquet (), François Delbot () and Christophe Picouleau ()
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Valentin Bouquet: Sorbonne Université
François Delbot: Sorbonne Université
Christophe Picouleau: CNAM

Annals of Operations Research, 2025, vol. 351, issue 1, No 21, 563-574

Abstract: Abstract Given a graph G and a non trivial partition $$(V_1,V_2)$$ ( V 1 , V 2 ) of its vertex-set, the satisfaction of a vertex $$v\in V_i$$ v ∈ V i is the ratio between the size of it’s closed neighborhood in $$V_i$$ 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.

Keywords: Vertex-partition; Edge-cut; Regular graph; Bipartite graph; Degree ratio; NP-complete (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10479-025-06615-7

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