A spectral minimal partition of a manifold is a decomposition into disjoint open sets that
minimizes a spectral energy functional. While it is known that bipartite minimal partitions …

Analyzing nodal domains is a way to discern the structure of eigenvectors of operators on a
graph. We give a new definition extending the concept of nodal domains to arbitrary signed …

We consider the normalized adjacency matrix of a random $ d $-regular graph on $ N $
vertices with any fixed degree $ d\geq 3$ and denote its eigenvalues as $\lambda_1= d/\sqrt …

Consider the normalized adjacency matrices of random $ d $-regular graphs on $ N $
vertices with fixed degree $ d\geq 3$, and denote the eigenvalues as $\lambda_1= d/\sqrt {d …

Large networks are useful in a wide range of applications. Sometimes problem instances
are composed of billions of entities. Decomposing and analyzing these structures helps us …

As a non-trivial extension of the celebrated Cheeger inequality, the higher-order Cheeger
inequalities for graphs due to Lee, Oveis Gharan and Trevisan provide for each $ k $ an …

This report documents the program and the outcomes of Dagstuhl Seminar 23331" Recent
Trends in Graph Decomposition", which took place from 13. August to 18. August, 2023. The …

Discrete graphs are ubiquitous models applicable to many areas, useful for any discrete
system with some notion of connectivity. Some examples for which these are useful are …

This report documents the program and the outcomes of Dagstuhl Seminar 23331 “Recent
Trends in Graph Decomposition”, which took place from 13. August to 18. August, 2023. The …