Geodesic
Discrete quantitative nodal theorem
László Lovász1
1Alfred Rényi Institute of Mathematics
The electronic journal of combinatorics, Tome 28 (2021) no. 3
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We prove a theorem that can be thought of as a common generalization of the Discrete Nodal Theorem and (one direction of) Cheeger's Inequality for graphs. A special case of this result will assert that if the second and third eigenvalues of the Laplacian are at least $\varepsilon$ apart, then the subgraphs induced by the positive and negative supports of the eigenvector belonging to $\lambda_2$ are not only connected, but edge-expanders (in a weighted sense, with expansion depending on $\varepsilon$).
DOI : 10.37236/9944
Classification : 05C50, 05C40, 15A18
Mots-clés : Cheeger's inequality for graphs, Laplacian of a connected graph

László Lovász  1

1 Alfred Rényi Institute of Mathematics 
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László Lovász. Discrete quantitative nodal theorem. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/9944

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