What does this research mean for the field?

The problem of achieving a hereditary graph property via a limited number of vertex splits is NP-complete for properties characterized by biconnected forbidden subgraphs, Bipartite-VS, and Perfect-VS, and its parameterized complexity is heavily driven by whether vertices can be split more than once. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to explore the computational complexity of achieving specific hereditary graph properties through vertex splitting operations.

July 24, 2026ACM Transactions on Computation TheoryOpen Access

On the Complexity of Establishing Hereditary Graph Properties via Vertex Splitting

View Full Paper

Ask AI

Bookmark

Authors

AFAlexander FirbasTU Wien MSManuel SorgeTU Wien

Discussion

Member takes

Implication

Randomized trial investigates computational complexity of hereditary graph properties through vertex splitting, suggesting new pathways for analysis.

Key Points

The aim is to explore the computational complexity of achieving specific hereditary graph properties through vertex splitting operations.
Classified complexity of Π-VS for properties defined by forbidden induced subgraphs of order ≤3.
Developed a framework for proving NP-completeness using forbidden subgraphs and prescribed vertex splits.
Studied parameterized complexity of Π-VS concerning the number of allowed vertex splits.
Demonstrated NP-completeness for F-Free-VS in biconnected graphs, under both forbidden subgraph conditions.
Established NP-completeness for infinite families like Bipartite-VS and Perfect-VS, contrasting known polynomial results for cycle sets.
Showed para-NP-hardness for Triangle-Free Vertex Splitting and developed an XP-algorithm when splits are limited to once per vertex.

Cite This Study

Firbas et al. (2026) studied this question.

synapsesocial.com/papers/6a62ffef395161722cd150b7 https://doi.org/10.1145/3831678

View Full Paper

Ask AI

Bookmark

Implication

Randomized trial investigates computational complexity of hereditary graph properties through vertex splitting, suggesting new pathways for analysis.

On the Complexity of Establishing Hereditary Graph Properties via Vertex Splitting

Discussion

Member takes

Implication

Key Points

Cite This Study

On the Complexity of Establishing Hereditary Graph Properties via Vertex Splitting

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider