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Extremal signed complete graphs with a K2,2-minor-free negative subgraph

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Research area:mathematics

What the study found

The authors characterize the extremal signed complete graphs that achieve the maximum and second maximum index, where the negative-edge-induced subgraph is K2,2-minor free. Here, a signed complete graph means a complete graph with edges labeled positive or negative, and the negative-edge-induced subgraph is the subgraph formed by the negative edges.

Why the authors say this matters

The abstract says that characterizing the extremum problem of the index of a signed complete graph is a concern in signed graphs. The study suggests this result helps address that extremal problem under the condition that the negative-edge-induced subgraph is K2,2-minor free.

What the researchers tested

The researchers studied a signed complete graph Γ = (K_n, H^-), where H^- is the negative-edge-induced subgraph. They examined the case in which H is a spanning subgraph of K_n that is K2,2-minor free, and they analyzed which signed complete graphs give the largest and second largest index.

What worked and what didn't

The abstract states that the extremal signed complete graphs achieving the maximum index were characterized. It also states that the extremal graphs achieving the second maximum index were characterized. No additional specific graph forms or comparisons are given in the abstract.

What to keep in mind

The available summary does not describe the exact characterization results or the mathematical form of the index. It also does not state limitations, examples, or applications beyond the K2,2-minor-free setting.

Key points

  • The paper studies signed complete graphs with negative edges forming a K2,2-minor-free subgraph.
  • It characterizes the graphs with the maximum index in this setting.
  • It also characterizes the graphs with the second maximum index.
  • The abstract frames this as part of an extremum problem in signed graphs.

Disclosure

Research title:
Extremal signed complete graphs with a K2,2-minor-free negative subgraph
Authors:
Mengyao Qin, Dan Li
Institutions:
Xinjiang University, Xinjiang University
Publication date:
2026-04-24
DOI:
10.1051/ro/2026047
OpenAlex record:
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AI provenance: This post was generated by gpt-5.4-mini (OpenAI). The original authors did not write or review this post.

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