A Spectral Erdős–Faudree–Rousseau Theorem

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Theorem presents spectral methods to count triangular edges in graphs, suggesting new applications in extremal graph theory.

Every graph with more vertices and edges has triangular edges, highlighting a key relationship in graph theory.
Proves that specific graphs contain at least such edges unless they are balanced complete bipartite graphs.
Application of spectral methods offers sharper bounds on graph parameters compared to previous research.
Insights from this research may advance understanding of counting triangles and stability in graphs.

Li et al. (2025) studied this question.

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View Full Paper

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Authors

Theorem presents spectral methods to count triangular edges in graphs, suggesting new applications in extremal graph theory.

Every graph with more vertices and edges has triangular edges, highlighting a key relationship in graph theory.
Proves that specific graphs contain at least such edges unless they are balanced complete bipartite graphs.
Application of spectral methods offers sharper bounds on graph parameters compared to previous research.
Insights from this research may advance understanding of counting triangles and stability in graphs.

Li et al. (2025) studied this question.

View Full Paper

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Bookmark