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arXiv · 2610.30859

The signless Laplacian spectral Turán problems for disjoint triangles

Ming-Zhu Chen·Ya-Lei Jin·Peng-Li Zhang
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Abstract

The classical Turán-type problem for graphs forbidding $k$ disjoint triangles has been resolved firstly by Erdős [Arch. Math. 13 (1962) 222-227] for graphs of sufficiently large order and improved by Moon [Canad. J. Math. 20 (1968) 95-102], who established that the unique edge extremal graph is $K_{k-1}\vee T_2(n-k+1)$ for $n> \frac{19k-11}{2}$. In this paper, we determine the maximum signless Laplacian spectral radius among all $kK_3$-free graphs of order $n$ and characterize the unique signless Laplacian spectral extremal graph $K_{k-1}\vee T_{2}(n-k+1)$ for all $k\ge 2$ and sufficiently large $n$.

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Ming-Zhu Chen, Ya-Lei Jin, Peng-Li Zhang. 2026-10-22. The signless Laplacian spectral Turán problems for disjoint triangles. https://arxiv.org/abs/2610.30859

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