Embeddings of K ₅ in the Torus

Lowell Abrams

doi:10.1080/00029890.2025.2533060

August 15, 2025American Mathematical Monthly

Embeddings of K ₅ in the Torus

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Key Points

There are exactly six embeddings of the complete graph on five vertices in the torus, uncovering a unique topological relationship.
The main finding addresses the isomorphism of the embeddings, indicating a structured connection between graph theory and topology.
Using an innovative approach, the study bridges concepts in combinatorics and topology to explore graph embeddings.
This research highlights the elegant interplay between mathematical fields, potentially informing future studies in topology and combinatorial structures.

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Implication

This analysis reveals six distinct embeddings of the complete graph in the torus, highlighting combinatorial and topological interactions.

Abstract

Using an approach that highlights the interaction of combinatorics and topology, we show that, up to isomorphism, there are exactly six embeddings of the complete graph on five vertices in the torus.

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Lowell Abrams (2025) studied this question.

synapsesocial.com/papers/68af59e3ad7bf08b1eadef0b https://doi.org/10.1080/00029890.2025.2533060

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Embeddings of K ₅ in the Torus

Key Points

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Implication

Abstract

Discussion

Cite This Study

Embeddings of K ₅ in the Torus

Key Points

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Implication

Abstract

Discussion

Cite This Study

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