326 papers
This paper generalizes the role of the abstract chromatic number in determining the asymptotics of Turán-type functions to other graph parameters, providing proofs and two specific examples of this extension.
This paper proves that there are only finitely many prime critically 4-frustrated and 5-frustrated signed graphs, thereby confirming the Steffen-Naserasr conjecture for the cases and .
This paper improves the known upper bounds on the maximum number of tangencies among 1-intersecting Jordan arcs from to for the general case and to for the strictly 1-intersecting case, while also establishing tighter bounds for specific variants involving -monotone curves and proving a new graph-theoretic result.
This paper presents the first polynomial-time and space decoding algorithms for bounded-weight de Bruijn sequences, which are subsequently applied to efficiently decode universal cycles for t-subsets and t-multisets.
This paper presents the first known efficient universal cycle constructions for k-subsets and k-multisets by introducing a new representation that enables successor-rule and necklace concatenation algorithms to generate these sequences in O(n) time per symbol and O(1) amortized time per symbol, respectively, for all n and k ≥ 2.
This paper introduces a new graph game called "Agents and Adversary," a variation of Cops and Robbers, by classifying infinite graph families as winning for either side, defining a new symmetry to establish an Adversary winning strategy, and providing tight bounds on the Agents' time-to-win.
This paper demonstrates that the second-order term in the scaling limit of the identity element for the abelian sandpile group on finite Sierpinski gasket graphs converges to the path distance to the nearest corner, a result established by decomposing the identity into a constant function and the Laplacian of the graph distance.
This paper introduces a maximum-entropy random walk framework for directed hypergraphs that models both broadcasting and merging interactions through a Kullback-Leibler divergence projection, utilizing Sinkhorn-type iterations to derive transition kernels and analyze ergodicity for capturing complex higher-order flows.
This paper derives new identities for Fibonacci, Lucas, and generalized Fibonacci sequences with multiple indices by applying symmetric polynomials to Binet's formula, resulting in expressions that combine powers of Lucas numbers with binomial coefficients.
This paper investigates the "evil twin property" in sums of wildflowers and mutant flowers within combinatorial game theory, identifying a maximal closed set of such games that possess this property and proving that determining their outcome classes is NP-hard.
This paper investigates triangular line arrangements on the projective plane by proving their combinatorics are always realized by Roots-of-Unity-Arrangements, establishing conditions for their freeness, and demonstrating that freeness is not determined solely by weak combinatorics.
This paper introduces a comprehensive generalization of the switch operation on -graphs, axiomatically studying its impact on homomorphisms to resolve open problems regarding categorical products and chromatic numbers, including explicit constructions and calculations for forests.
Using the compression method, this paper generalizes lower bounds for the Erdős unit distance and distinct distance problems to higher dimensions ( for ), providing alternative proofs and establishing new estimates for the number of distinct distances.
This paper proves the nonexistence of Heronian triangles with three integer medians by deriving a universal identity for arbitrary triangles and establishing a lemma demonstrating that such triangles, if they existed, would necessarily occur in non-similar pairs.
This paper analyzes a two-player permutation game inspired by the Erdős-Szekeres Theorem, determining the winner and providing a winning strategy for cases where the parameter is greater than or equal to and is an integer between 2 and 5.
This paper presents the construction of a 2-distance set consisting of 277 points in 23-dimensional Euclidean space, where the pairwise distances between points are restricted to the values 2 and .
The paper establishes that any collection of hyperplanes covering the vertices of an -dimensional hypercube, where each vertex is covered by a hyperplane involving every coordinate variable, must contain at least hyperplanes, a result that generalizes the skew covers problem and yields tight bounds for slicing hypercube edges with bounded integer coefficients.
This paper establishes elementary upper and lower bounds for the partition function and its generalizations by applying a geometric inequality in Euclidean space.
This paper proposes and rigorously establishes a symmetrization relation between 4d BPS quivers and 3d symmetric quivers, demonstrating that the wall-crossing structure of 4d Argyres-Douglas theories is isomorphic to the unlinking of their 3d counterparts and that these symmetric quivers successfully capture the Schur indices of the original 4d theories.
This paper establishes the NP-completeness of determining whether graphs lacking efficient edge dominating sets possess at least two perfect edge dominating sets, while also presenting a cubic-time algorithm to find, count, and weight minimal perfect edge dominating sets in -free graphs.