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arXiv · 2306.06655

Turán problem for $\mathcal{K}_4^-$-free signed graphs

Fan Chen·Xiying Yuan
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Abstract

Suppose that $\dot{G}$ is an unbalanced signed graph of order $n$ with $e(\dot{G})$ edges. Let $ρ(\dot{G})$ be the spectral radius of $\dot{G}$, and $\mathcal{K}_4^-$ be the set of the unbalanced $K_4$. In this paper, we prove that if $\dot{G}$ is a $\mathcal{K}_4^-$-free unbalanced signed graph of order $n$, then $e(\dot{G})\leqslant \frac{n(n-1)}{2}-(n-3)$ and $ρ(\dot{G})\leqslant n-2$. Moreover, the extremal graphs are completely characterized.

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Fan Chen, Xiying Yuan. 2023-06-11. Turán problem for $\mathcal{K}_4^-$-free signed graphs. https://arxiv.org/abs/2306.06655

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