Yuejian Peng

Z.Yan, and Y.Peng, “A Strong Structural Stability of C2k+1 ${C}_{2k+1}$-Free Graphs,” Journal of Graph Theory0 (2026): e70022. https://doi.org/10.1002/jgt.70022. 1 Introduction For a graph G $G$ , let V ( G ) $V(G)$ and E ( G ) $E(G)$ denote the vertex set and the edge set of G $G$ , respectively. Write e ( G ) = ∣ E ( G ) ∣ $e(G)=| E(G)| $ for the number of edges of a graph G $G$ .

A well-known theorem of Mantel states that every -vertex graph with more than edges contains a triangle. An interesting problem in extremal graph theory studies the minimum number of edges contained in triangles among graphs with a prescribed number of vertices and edges. Erdős, Faudree, and Rousseau (1992) showed that a graph on vertices with more than edges contains at least edges in triangles. Such edges are called triangular edges.

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