This paper introduces a local-to-global method for analyzing low influence functions on simplicial complexes and proves a local-to-global KKL-type Theorem.

The paper presents a novel and significantly faster algorithm for computing the second discrete homology group of a graph by identifying five basic quotient shapes of the 3-cube.

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…

Ramos and White's theorem on multiplicity stability of rational homology for configuration spaces of certain graphs is extended and computed for various families of graphs using computer algebra.

This paper presents an algorithmic framework for exhaustively generating and tabulating knot and link diagrams on the thickened torus.

This paper defines and investigates ample sets of Cartesian products using minor-subproducts and provides characterizations of ampleness, including equivalence to ampleness of complement, superisometr…

This paper generalizes the Phoa principle in synthetic domain theory to transfinite cases, introduces sobriomorphisms, and proposes a hypothetical completeness theorem.

This paper proves that the minimum edge-outerplanarity of a planar graph can be computed in polynomial time.

This paper constructs a cubic graph with a polyhedral map whose automorphism groups are isomorphic to a given finite group.

The paper introduces a computational framework using Hodge zero-modes to track the geometry of topological features in parameter-dependent data, providing metrics like curvature and holonomy to quanti…

This paper studies the complexity of the Flood-It game on various graph classes and provides polynomial-time algorithms for Free Flood-It on graphs free of certain jewels, while proving NP-completenes…

The paper shows that an oddomorphism between graphs does not imply graph minor containment and introduces a new structural relation called split-off minor.

This paper shows that finding the minimum geodetic set in chordal graphs is fixed parameter tractable, implying a polynomial-time algorithm for k-trees. It also proves that the problem is NP-hard on i…

This paper proves that counting quasi-trees in a connected ribbon graph is #P-complete.

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.

The paper constructs Schubert subspace codes with maximum possible size in certain extremal distance cases using two methods: direct-sum decomposition and field reduction.

This paper simplifies the proof of the bound on the target dimension for reducing the dimension of high-dimensional polygonal curves using random projections, extending it to various distance measures…

This paper proves that testing the equivalence of finite closure systems specified by implicational and intersection methods is coNP-complete.