316 papers
This paper investigates how algebraic invariants of edge ideals change under selective graph suspensions, demonstrating that while suspensions over minimal vertex covers consistently preserve regularity and increase projective dimension by one, suspensions over maximal independent sets exhibit uniform behavior only for paths and cycles, with a specific extremal family of paths showing increases in both regularity and the -invariant.
This paper establishes a systematic framework for constructing digraph-defined external difference families by combining graph blow-up techniques with generalized vertex labellings, resulting in new combinatorial families—including the first infinite construction for specific 2-circular external difference families—and novel results on graph labellings such as -valuations for sun graphs.
This paper introduces a dynamic programming framework to identify extremal general polyomino chains for degree-based topological indices, specifically resolving a 2015 open problem by characterizing the chains that maximize the generalized Randić index with based on the number of squares modulo 4.
This paper characterizes strong -matroids corresponding to orientable ribbon graphs via the new concept of pseudo-orientable ribbon graphs, establishes a geometric construction linking them to orientable graphs, and derives significant results including the Matrix--Quasi-tree Theorem, Hurwitz stability, and log-concavity for quasi-tree generating polynomials.
This paper introduces color 2-switches to characterize -colored graphs with identical color degree matrices and defines several classes of neighborhood -balanced graphs to analyze their structural properties and minimum balance numbers across various graph families.
This paper presents the first part of a study on the generalized Honeymoon Oberwolfach Problem by establishing existence conditions for solutions involving multiple round tables, specifically for cases with two round tables under certain modular constraints and for cases with small round tables where the total number of non-spouse seats is at most 10.
This paper proves that for connected outerplanar graphs containing at most one or two triangles, any precoloring of two or three non-adjacent vertices can be extended to a proper 3-coloring of the entire graph.
This paper presents a simplified extension of Birkhoff's representation theorem to locally-finite distributive lattices, establishing an isomorphism between such a lattice and the order ideals of the poset of its prime filters that differ from a specific ideal by a finite set.
This paper establishes a necessary and sufficient condition for decomposing the complete graph on vertices into isomorphic copies of a Cayley graph on a CI-group , while also providing a constructive method for such factorizations.
This paper investigates the structural implications of vanishing -degree Turán densities in hypergraphs, proving that for -uniform hypergraphs with vanishing 2-degree Turán density, a specific global vertex ordering (2-vanishing order) must exist, thereby generalizing classical results on zero Turán density and demonstrating that unlike the classical case, 2-degree Turán densities accumulate at zero.
This paper employs tropical geometry and Hamiltonian flows to derive explicit formulae for leaky Hurwitz numbers in genus 0 and prove that these invariants satisfy topological recursion under fixed leakiness, thereby establishing a partial inverse to recent results on KP -functions.
This paper constructs new infinite families of Ramanujan complexes with distinct local structures by utilizing super-definite unitary groups over totally real number fields, yielding novel examples across various types and providing a fully explicit rank-5 construction that generates golden gates for the real Lie group .
This paper establishes a precise asymptotic transfer mechanism for critical recursive composition schemes in map enumeration, demonstrating how singular structures and associated central limit theorems for statistics on 2-connected maps propagate to the broader class of all maps.
This paper resolves the open question regarding cyclic permutations that avoid the decreasing pattern and the pattern by deriving explicit formulas through an analysis of cycle form structures and the application of Dilworth's theorem.
This paper investigates a five-sequence of adjoint functors induced by functions between vertex sets of simplicial complexes, utilizing this structure to establish three categorical frameworks where the Stanley-Reisner correspondence yields dualities with commutative monomial rings.
This paper establishes new Ore-degree conditions that guarantee the existence of matchings in -uniform hypergraphs by proving upper bounds on the Ore-degree for intersecting hypergraphs and demonstrating that exceeding a specific threshold ensures the presence of pairwise disjoint edges.
This paper combines additive combinatorics and Diophantine geometry to establish a uniform sum-product phenomenon for one-dimensional algebraic groups over , thereby resolving Bremner's conjecture on arithmetic progressions in elliptic curve coordinates and improving upon existing results by Bays--Breuillard regarding Elekes--Szabó-type theorems.
This paper addresses the DNA coverage depth problem by developing combinatorial tools based on duality and extended weight enumerators to derive closed formulas for specific linear codes and a general expression linking coverage depth to the weight distributions of higher-field extensions.
This paper introduces a nonparametric Weighted Random Dot Product Graph (WRDPG) model that extends traditional network analysis by using latent positions and moment-generating functions to capture higher-order edge weight distributions beyond the mean, while providing consistent estimation guarantees and a generative framework for sampling weighted graphs.
This paper establishes a systematic connection between the -dimensional Prouhet--Tarry--Escott problem and combinatorial design theory, introducing new solution definitions, proving fundamental bounds, and developing construction methods using block designs and orthogonal arrays that generalize and unify numerous previous results.