This paper shows that for every fixed length t, cycles Ct and thetas Θt have the induced Erdős--Pósa property with respect to the induced minor relation in graphs.

This paper shows that for every graph, there exist a certain number of vertex-disjoint cycles of different lengths, or a smaller set of vertices such that the graph without these vertices has fewer cy…

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 investigates the complexity of recognizing domatically critical graphs, which are graphs with maximum dominating sets that cannot be increased by deleting any edge.

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 introduces minimal additive codes over Fqh and establishes a one-to-one correspondence between minimal additive codes and additive strong blocking sets. It also compares this framework with…

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.

This paper unconditionally proves the Orthogonal Vectors and Monotone Orthogonal Vectors conjectures in concrete computational models, and provides stronger lower bounds for Boolean formulas and branc…

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 provides the first unconditional proof for Weber's Conjecture for the case $k ext{ up to } 12$, which is crucial for lattice-based cryptography.

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

This paper uses local flag algebra to prove bounds on the strong chromatic index of graphs, making progress towards established conjectures for general, bipartite, and asymmetric bipartite graphs.

This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.

This paper shows that finite unions of intersecting affine modules in one dimension are efficiently exactly learnable using equivalence and subset queries.

This paper identifies new, algebraically weak classes of instances for the Linear Equivalence Problem (LEP) by generalizing techniques from the Permutation Equivalence Problem (PEP) using power codes…