Two-place Laplacian matching root integral variations are impossible
Combinatorics
2026-05-05 v1
Abstract
Wang, Cui, and Cioab\u{a} introduced the Laplacian matching root integral variation of a graph and proved that it cannot occur in one place. They also showed that the two-place variation is impossible for connected graphs satisfying , where is the girth and is the dimension of the cycle space, and conjectured that no connected graph admits such a two-place variation. In this paper, we confirm this conjecture. The proof combines a structural relation obtained in their paper with two new power-sum identities for Laplacian matching roots.
Cite
@article{arxiv.2605.01760,
title = {Two-place Laplacian matching root integral variations are impossible},
author = {Sebastian M. Cioabă and Lele Liu and Yi Wang},
journal= {arXiv preprint arXiv:2605.01760},
year = {2026}
}