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arXiv · 2605.01760

Two-place Laplacian matching root integral variations are impossible

Sebastian M. Cioabă·Lele Liu·Yi Wang
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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 $g(G)/c(G)>7/6$, where $g(G)$ is the girth and $c(G)$ 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.

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Sebastian M. Cioabă, Lele Liu, Yi Wang. 2026-05-03. Two-place Laplacian matching root integral variations are impossible. https://arxiv.org/abs/2605.01760

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