This paper characterizes acyclic hypergraphs according to whether they admit unique canonical join trees as root and provides a linear-time algorithm to construct them.

This paper introduces online assignment policies for stochastic matching on hypergraphs, which are maximally stable and allow for the derivation of necessary and sufficient stability criteria.

This paper determines the linear Tur'an numbers for higher uniformity $r$-uniform linear hypergraphs and studies specific cases such as stars, hypertrees, and paths.

This paper introduces a new way to represent finite posets as subwords of finite words in categories, and characterizes the monic categories that admit this representation.

This paper characterizes stabilizability of stochastic dynamic matching on hypergraphs using the arrival rates and incidence matrix, and proposes a stabilizing policy.

This paper studies the maximum size of an independent set in the discrete simplex graph and provides new bounds using translated smaller graphs and finite rational linear systems.

This paper introduces ZipLine, a system for integrative analysis of multivariate graphs through a unified predicate language and learning algorithm.

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

This paper studies set-defined graph classes and proves that bounded unions of shift-colorable graphs form the fundamental obstruction to chromatic number boundness in these classes.

This paper studies the NP-completeness and provides a polynomial-time algorithm for the disjoint separators problem in planar graphs when all sizes are equal to one.

This paper shows #P-completeness for several graph counting problems using a new technique.

The paper formalizes Razborov's flag algebra method for finite simple graphs and creates a compiler to transform certificate data into algebraic proofs checked by Lean.

This paper introduces HySpecPro, a single-level hypergraph partitioner that performs end-to-end optimization in a spectral embedding space, delivering cut quality comparable to multilevel methods with…

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