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- W4318153447 abstract "The generalized conductance $phi(G,H)$ between two graphs $G$ and $H$ on the same vertex set $V$ is defined as the ratio $$ phi(G,H) = min_{Ssubseteq V} frac{cap_G(S,bar{S})}{ cap_H(S,bar{S})}, $$ where $cap_G(S,bar{S})$ is the total weight of the edges crossing from $S$ to $bar{S}=V-S$. We show that the minimum generalized eigenvalue $lambda(L_G,L_H)$ of the pair of Laplacians $L_G$ and $L_H$ satisfies $$ lambda(L_G,L_H) geq phi(G,H) phi(G)/8, $$ where $phi(G)$ is the usual conductance of $G$. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to $lambda(L_G,L_H)$. The inequality complements a recent proof that $phi(G)$ cannot be replaced by $Theta(phi(G,H))$ in the above inequality, unless the Unique Games Conjecture is false." @default.
- W4318153447 created "2023-01-26" @default.
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- W4318153447 date "2014-10-22" @default.
- W4318153447 modified "2023-09-29" @default.
- W4318153447 title "A Generalized Cheeger Inequality" @default.
- W4318153447 doi "https://doi.org/10.48550/arxiv.1412.6075" @default.
- W4318153447 hasPublicationYear "2014" @default.
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