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math.CO2026
Spectral Extremal Graphs without a -Factor
Cunxiang Duan, Tingting Han, Lin-Peng Zhang
Let and let . A -factor in an -vertex graph is a collection of vertex-disjoint copies of that covers the entire vertex set. We determine the maximu…
math.CO2026
An Ore-type condition for -tilings in graphs
Yuping Gao, Yilin Guo, Guanghui Wang +1
A graph admits an -tiling if it contains a collection of vertex-disjoint copies of . In this paper, we confirm a conjecture proposed by Kühn, Osthus, and Treglown by show…
math.CO2026
Extremal Laplacian energy of -free digraphs
Xiuwen Yang, Lin-Peng Zhang
The Laplacian energy of a digraph is defined as , where are the eigenvalues of the Laplacian matrix of . A (di)graph is said to be -free if…