Two-place Laplacian matching root integral variations are impossible
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909011353272320 |
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| author | Cioabă, Sebastian M. Liu, Lele Wang, Yi |
| author_facet | Cioabă, Sebastian M. Liu, Lele Wang, Yi |
| contents | Wang, Cui, and Cioabă 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01760 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-place Laplacian matching root integral variations are impossible Cioabă, Sebastian M. Liu, Lele Wang, Yi Combinatorics Wang, Cui, and Cioabă 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. |
| title | Two-place Laplacian matching root integral variations are impossible |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.01760 |