This paper introduces DiPhon, a diffusion framework for size-scalable graph generation, using a continuous diffusion process on the graphon space and a discretized graph-level process.

This paper addresses the problem of inferring a directed network from nodal measurements using graph convolutional filters and identifies the diffusion filter and network topology.

This paper settles the complexity of three sketching problems in graphs and distributions.

A new polynomial-time algorithm is presented for optimally coloring perfect graphs using graph-theoretic operations and iterative walk counting.

The paper introduces a diffusion-based uncertainty model for robust optimization on graphs, showing that the resulting computational complexity depends critically on the interaction between the uncert…

The paper proves XNLP-hardness of Directed Edge Geography and Undirected Edge Geography when parameterized by pathwidth, and shows their fixed-parameter tractability when parameterized by treewidth an…

This paper proposes two algorithms for approximating the number of four-cycles in graph edge streams, improving upon existing theoretical bounds and handling non-concentrated four-cycles in one-pass.

The paper investigates the relationship between graph classes, edit cost functions, and computational complexity of the graph edit distance, providing polynomial-time reductions and correspondences.

This paper proposes a fairness-aware adaptation of graph-based diffusion methods by modifying the Laplacian operator to mitigate bias-related components.

This paper studies the triangle-densest-$k$-subgraph problem in an average-case model and proposes spectral and semidefinite algorithms for its recovery.

Chen et al. prove a Poincaré inequality for Glauber dynamics of hard-core model on random regular graphs using Bochner--Bakry--Émery approach.

This paper studies stochastic multi-armed bandits on dynamic graphs with local movement constraints and establishes sublinear expected regret.

The paper shows that every problem asking if a given graph has an edge-coloring without an edge-colored clique from a fixed family is poly-time equivalent to a Constraint Satisfaction Problem, resulti…

This paper studies the depth required for a graph neural network on a sparse graph using the contextual stochastic block model, and proves that the error is governed by the Kesten-Stigum ratio.

This paper studies the structural expressivity and parameterized complexity of counting homomorphisms from small temporal patterns to large temporal graphs, proving a temporal Lovász-style theorem, in…