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arXiv · 2606.14381

The maximum number of edges in $C_{2k+1}^{-}$-free unbalanced signed graphs with bounded clique number

Junjie Wang·Yaoping Hou
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Abstract

Recently, the Tur\'{a}n problem for graphs with bounded clique number has attracted considerable attention. Since a graph can be regarded as a signed graph without negative edges, it is natural to extend the study of such Tur\'{a}n-type problems to signed graphs. With this motivation, we investigate the Tur\'{a}n-type problem for unbalanced $C_{2k+1}^{-}$-free signed graphs with bounded clique number. In fact, we establish a general result via the classical stability theorem. Specifically, for sufficiently large $n$ and a color-critical graph $F$, we determine the maximum number of edges among all $n$-vertex $C_{2k+1}^{-}$-free unbalanced signed graphs whose underlying graphs are $F$-free.

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Junjie Wang, Yaoping Hou. 2026-06-12. The maximum number of edges in $C_{2k+1}^{-}$-free unbalanced signed graphs with bounded clique number. https://arxiv.org/abs/2606.14381

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