Year: 2026
Type: preprint
Abstract: Let $b(n)$ denote the minimum number of perfect matchings in a simple brace of order $n$. De~Carvalho, Lucchesi and Murty (SIAM Journal on Discrete Mathematics, 27(2): (2013) 940-958) proved that $b(n)\ge(n-2)^2/8$ and conjectured that $b(n)=(n-2)^2/4$ for all sufficiently large even $n$. We prove this conjecture.
Source: arXiv (Cornell University)
Authors: Feng, Xing, Zhou, Jinqiu
Institution: Jimei University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G6910113313
OpenAlex ID: W7221520233