On the bipartition of graphs
Copyright policy )On the bipartition of graphs
The isoperimetric constant \(i(G)\) of a cubic graph \(G\) is \(i(G)=\min | \partial U| /| U|\) where \(|\cdot|\) is cardinality, \(U\) runs over all subsets of the vertex set \(VG\) satisfying \(| U| \leq \frac12 | VG|\), and \(| \partial U|\) is the number of edges running from \(U\) to the complement \(VG\backslash U\). The spectral theory on Riemann surfaces is used to prove that infinitely many cubic graphs \(G\) exist satisfying \(i(G)\geq 1/128\).
- École Polytechnique Fédérale de Lausanne EPFL Switzerland
Extremal problems in graph theory, isoperimetric problems, Applied Mathematics, Spectral problems; spectral geometry; scattering theory on manifolds, Discrete Mathematics and Combinatorics, cubic graphs, eigenvalues of the Laplacian
Extremal problems in graph theory, isoperimetric problems, Applied Mathematics, Spectral problems; spectral geometry; scattering theory on manifolds, Discrete Mathematics and Combinatorics, cubic graphs, eigenvalues of the Laplacian
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