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Partition of graphs with maximum degree ratio

Author

Listed:
  • Valentin Bouquet

    (Sorbonne Université
    UPL, Université Paris Nanterre)

  • François Delbot

    (Sorbonne Université
    UPL, Université Paris Nanterre)

  • Christophe Picouleau

    (CNAM)

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.

Suggested Citation

  • Valentin Bouquet & François Delbot & Christophe Picouleau, 2025. "Partition of graphs with maximum degree ratio," Annals of Operations Research, Springer, vol. 351(1), pages 563-574, August.
    • Handle: RePEc:spr:annopr:v:351:y:2025:i:1:d:10.1007_s10479-025-06615-7
    DOI: 10.1007/s10479-025-06615-7
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    References listed on IDEAS

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    1. Bazgan, Cristina & Tuza, Zsolt & Vanderpooten, Daniel, 2010. "Satisfactory graph partition, variants, and generalizations," European Journal of Operational Research, Elsevier, vol. 206(2), pages 271-280, October.
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