PreprintCC BY 4.0arXiv
The signless Laplacian spectral Turán problems for disjoint triangles
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 Kk−1∨ T2(n−k+1) for n> (19k−11)/2. In this paper, we determine the maximum signless Laplacian spectral radius among all kK3-free graphs of order n and characterize the unique signless Laplacian spectral extremal graph Kk−1∨ T2(n−k+1) for all k≥ 2 and sufficiently large n.
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BibTeX
@misc{chen2026signless,
title = {{The signless Laplacian spectral Turán problems for disjoint triangles}},
author = {Ming-Zhu Chen and Ya-Lei Jin and Peng-Li Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30859},
eprint = {2610.30859},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30859},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The signless Laplacian spectral Turán problems for disjoint triangles
AU - Ming-Zhu Chen
AU - Ya-Lei Jin
AU - Peng-Li Zhang
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30859
UR - https://arxiv.org/abs/2610.30859
AB - 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∨ T_2(n−k+1) for n> (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∨ T_2(n−k+1) for all k≥ 2 and sufficiently large n.
ER -