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Partitioning vertices and edges of graphs into connected subgraphs

Author

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  • Baudon, Olivier
  • Bensmail, Julien
  • Vayssieres, Lyn

Abstract

Arbitrarily partitionable (AP) graphs are graphs that can have their vertices partitioned into arbitrarily many parts inducing connected graphs of arbitrary orders. Since their introduction, several aspects of AP graphs have been investigated in literature, including structural and algorithmic aspects, their connections with other fundamental notions of graph theory, and variants of the original notion. Quite recently, an edge version of AP graphs, called arbitrarily edge-partitionable (AEP) graphs have been introduced and studied, with a special focus on their similarities and discrepancies with AP graphs.

Suggested Citation

  • Baudon, Olivier & Bensmail, Julien & Vayssieres, Lyn, 2025. "Partitioning vertices and edges of graphs into connected subgraphs," Applied Mathematics and Computation, Elsevier, vol. 505(C).
    • Handle: RePEc:eee:apmaco:v:505:y:2025:i:c:s0096300325002577
    DOI: 10.1016/j.amc.2025.129531
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    References listed on IDEAS

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    1. Julien Bensmail, 2015. "On the complexity of partitioning a graph into a few connected subgraphs," Journal of Combinatorial Optimization, Springer, vol. 30(1), pages 174-187, July.
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