292 papers
This paper introduces the family of -disjoint graphs as a generalization of non-König-Egerváry almost bipartite graphs, proving that they preserve key structural equalities while extending the relationship between the corona, core, and independence number to accommodate multiple disjoint odd cycles, thereby verifying a recent conjecture by Levit and Mandrescu.
This paper characterizes Sterboul–Deming graphs—defined as graphs where every vertex belongs to a posy or a flower—by providing constructive decomposition algorithms for graphs with perfect or unique perfect matchings, extending the analysis via Gallai–Edmonds decomposition, and demonstrating that the class encompasses all graphs possessing a -factor.
This paper introduces generalized Jflower and Jposy configurations that unify with classical flower and posy structures to provide a comprehensive characterization of Sterboul-Deming graphs, where every vertex belongs to a specific configuration relative to a maximum matching.
This paper investigates biased Maker-Breaker games on systems of graphs where Maker aims to construct rainbow structures, specifically determining the threshold bias for rainbow connectivity and diameter games on complete graphs while disproving a conjecture by Balogh, Martin, and Pluhár.
This paper proves a conjecture by D'haeseleer, Metsch, and Werner by determining the largest cocliques and establishing a stability result for the Kneser graph of -flags in PG when is sufficiently large, utilizing the Erdős-Matching theorem for vector spaces.
This paper establishes that the space of infinite circle patterns in the Euclidean plane parameterized by discrete harmonic functions of finite Dirichlet energy forms an infinite-dimensional Hilbert manifold homeomorphic to the Sobolev space of half-differentiable functions, equipped with a Riemannian metric derived from a hyperbolic volume functional that relates to a symplectic form via an analogue of the Hilbert transform, thereby connecting these patterns to the Weil-Petersson class of the universal Teichmüller space.
This paper computes the magic labeling enumeration function and its generating function for pseudo-line and pseudo-cycle graphs, thereby extending previous work by Bóna et al. and providing explicit solutions where Stanley's theorem only guarantees a polynomial structure.
This paper investigates the structural and combinatorial properties of Bi-Cayley graphs over cyclic groups of order , establishing that they are connected, biregular, have girth three and diameter five, while also extending these findings to arbitrary finite groups under specific conditions.
This paper presents the first construction of a complex Hadamard matrix of order 94 by modifying a fundamental block method to utilize specific circulant -matrices of order 47, which were identified through computer-aided search.
This paper establishes that (odd hole, hammer, )-free graphs are perfectly divisible and provides specific polynomial and linear bounds on the chromatic number for various classes of short-holed graphs.
The paper proves that every graph with a minimum degree of at least $10^810^8K_{k+1}$, thereby resolving a long-standing problem posed by Kühn and Osthus.
This paper develops a theory of flats and hyperplane arrangements for matroids over tracts (T-matroids), establishing cryptomorphic descriptions via lattices of T-flats, hyperplane and point-line arrangements, and quiver representations, with applications to tropical linear spaces.
This paper establishes precise formulas for various topological indices and graph polynomials, including diameters, perfect matchings, Tutte polynomials, and Wiener and Szeged indices, for the infinite family of Schreier graphs generated by tree automaton groups.
This paper presents an integer linear programming model to formalize the rules of the Nikoli puzzle Evolomino and introduces an algorithm for generating unique instances, demonstrating that state-of-the-art solvers can efficiently solve grids up to 18x18.
This paper establishes a quantitative form of the Green-Tao theorem for sparse sets by proving that any subset of primes with relative density lacking nontrivial arithmetic progressions of length must satisfy , an improvement achieved through a new quasipolynomial inverse theorem and a dense model theorem.
This paper investigates the structure of the space of -invariant 3-paths in directed graphs by proving they admit a basis of trapezohedral paths and their merging images, thereby providing an explicit construction and an algorithm to compute their dimension and basis.
This paper establishes an analogue of the Robinson--Schensted correspondence for cylindric tableaux by constructing a bijection between specific pattern-avoiding permutations and pairs of cylindric standard Young tableaux, leading to new enumerative results and asymptotic formulas.
This paper investigates the real roots of graph reliability polynomials, proving that almost every graph possesses a nonreal reliability root and that these polynomials have roots dense on the interval where .
This paper establishes limit theorems for the number of fixed points, descents, and inversions in iterated random-to-top shuffles by employing analytical methods and novel combinatorial decompositions, thereby resolving open questions posed by Diaconis, Fulman, and Pehlivan.
This paper proves Lam's conjecture that the ABCT variety is a positive geometry by analyzing its combinatorial and algebraic structure, interpreting its boundary subvarieties as point configurations on , and constructing a top-degree meromorphic form.