Extends interior polynomial to signed bipartite graphs and connects to HOMFLY polynomial.
problem Invariants of signed bipartite graphs and their relation to HOMFLY polynomial.
method Extending interior polynomial to signed bipartite graphs and showing equality to HOMFLY polynomial part.
result Interior polynomial of signed bipartite graphs equals part of HOMFLY polynomial for planar case.
Formula for interior polynomial of bipartite graphs derived from knot theory.
problem Deriving a formula for the interior polynomial of bipartite graphs.
method Applied knot theory, Ehrhart reciprocity, flyping and mutation.
result Proved a mirroring formula for the interior polynomial of bipartite graphs.
This paper presents an algorithm to construct a weighted adjacency matrix of a plane bipartite graph obtained from a pretzel knot diagram. The determinant of this matrix after evaluation is shown to be the Jones polynomial of the pretzel knot by way of perfect matchings (or dimers) of this graph. The weights are Tutte'…
The paper studies eigenvalues and Cheeger constants on symmetric graphs.
problem Characterizing eigenvalues and Cheeger constants on symmetric graphs.
method Characterization of the first eigenfunction via sign condition, and calculation of Cheeger constants using the limit of p-Laplacian eigenvalues. result Identifies Cheeger constants of symmetric graphs and their quotients.
New research finds six bipartite intrinsically knotted graphs with 23 edges.
problem Identifying intrinsically knotted bipartite graphs with 23 edges.
method Analyzing embeddings and graph minors to find minimal intrinsically knotted graphs.
result No minor minimal intrinsically knotted bipartite graph exists with 23 edges.
Bipartite graphs with more edges than a threshold have positive curvature.
problem Determining the curvature of bipartite graphs based on edge density.
method Using a new formula for Lin--Lu--Yau curvature, the study establishes conditions for bipartite graphs to have positive curvature.
result Bipartite graphs with more edges than the specified threshold have positive Lin--Lu--Yau curvature.
Cascade-BGNN efficiently learns node representations for large-scale bipartite graphs.
problem Efficiently learning node representations for large-scale bipartite graphs with limited labels.
method Cascade-BGNN uses customized Inter-domain Message Passing (IDMP) and Intra-domain Alignment (IDA) for efficient information aggregation.
result Cascade-BGNN achieves domain-consistent, self-supervised, and efficient node representation learning.
The study extends Tutte's conflict graph concept to nonplanar graphs.
problem Understanding the structure of nonplanar graphs through conflict graphs.
method Defining a signed conflict graph for maximally planar subgraphs and analyzing their balance.
result For graphs with a flat embedding, every maximal planar subgraph has unbalanced conflict graphs if and only if the graph is intrinsically linked.
Proves Khovanov homology has no torsion for bipartite circle graphs.
problem Proving properties of Khovanov homology for bipartite circle graphs.
method Proved homotopy equivalence of independence complexes to wedges of spheres.
result Extreme Khovanov homology has no torsion.
Improved text summarization using belief propagation on weighted bipartite graphs.
problem Text summarization from a graph theory perspective.
method Generalized belief propagation algorithm for weighted bipartite graphs.
result Our algorithm outperforms greedy methods in text summarization tasks.
A graph is intrinsically knotted if every embedding contains a knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, K7 and the 13 graphs obtained from K7 by ∇Y moves, are the only minor minimal intrinsically knotted graphs with 21 edges. This set incl…
New method for matching bipartite and unipartite graphs without collapsing.
problem Matching between bipartite and unipartite networks without losing information.
method Formulated as an undirected graphical model, aligns graphs without collapsing.
result Consistent method with conditions for exact recovery of matching solution.
Researchers compute connectivity of braid group in bipartite graph configuration space.
problem Understanding connectivity of braid group in complex configuration space.
method Analysis of topology, hidden symmetry, and literature results.
result Explicit computation of connectivity at infinity for braid group.
We define integral odd Khovanov homology of principally unimodular bipartite graph-links.
We present evidence in support of a conjecture that a bipartite graph with at least five vertices in each part and |E(G)| \geq 4 |V(G)| - 17 is intrinsically knotted. We prove the conjecture for graphs that have exactly five or exactly six vertices in one part. We also show that there is a constant C_n such that a bipa…
We characterize which automorphisms of an arbitrary complete bipartite graph Kn,m can be induced by a homeomorphism of some embedding of the graph in S3.
Incorrect parity-based descriptions of realizable Gauss diagrams found, but bipartite graphs provide a valid approach.
problem Incorrect descriptions of realizable Gauss diagrams using parity conditions.
method Used bipartite graphs to describe realizable Gauss diagrams.
result Realizable Gauss diagrams can be accurately described using bipartite graphs.
The symmetries of complex molecular structures can be modeled by the {\em topological symmetry group} of the underlying embedded graph. It is therefore important to understand which topological symmetry groups can be realized by particular abstract graphs. This question has been answered for complete graphs; it is natu…
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links…
We study the Thurston-Bennequin number of complete and complete bipartite Legendrian graphs. We define a new invariant called the total Thurston-Bennequin number of the graph. We show that this invariant is determined by the Thurston-Bennequin numbers of 3-cycles for complete graphs and by the Thurston-Bennequin number…
New explicit constructions of unbalanced Ramanujan bipartite graphs.
problem Constructing bipartite Ramanujan graphs with specified degrees and avoiding certain edges.
method Presented explicit constructions and discussed known methods for Ramanujan graph construction.
result Affirmative answer to constructing unbalanced Ramanujan bipartite graphs under certain conditions.
Improved bipartite link prediction using 2-hop paths.
problem Link prediction in bipartite networks without node attributes.
method Multiply reconstructed adjacency matrix with symmetrically normalized training adjacency matrix to form 2-hop paths.
result 2-hop paths improve link prediction performance.
New model for detecting communities in weighted bipartite networks.
problem No model for community detection in overlapping bipartite weighted networks.
method Introduces BiMMDF model allowing any distribution with block structure.
result Efficient algorithm with theoretical guarantee of consistent estimation.
New tests detect communities in dense bipartite graphs with high accuracy.
problem Detecting communities in dense bipartite graphs with high accuracy.
method Non-asymptotic upper and lower bounds, novel minimax-optimal tests, hard-thresholded nonlinear statistics.
result Non-asymptotic upper and lower bounds match for any configuration of graph sizes.
The study proves conjecture for specific Artin groups.
problem Proving conjecture about Artin groups' properties.
method Analyzing Artin groups associated to triangle-free graphs and cones over square-free bipartite graphs.
result Proves conjecture for specific Artin groups.
We give an algorithmic computation for the height of Kauffman's clock lattice obtained from a knot diagram with two adjacent regions starred and without crossing information specified. We show that this lattice is more familiarly the graph of perfect matchings of a bipartite graph obtained from the knot diagram by over…
We generalize the construction of the Heegaard Floer homology for a singular knot to that for a balanced bipartite graph. For a given graph, we provide a combinatorial description of the Euler characteristic of its Heegaard Floer homology by using the "Kauffman states" on a graph diagram.
Temperley-Lieb algebras have been generalized to sl(3) web spaces. Since a cubic bipartite planar graph with suitable directions on edges is a web, the quantum sl(3) invariants naturally extend to all cubic bipartite planar graphs. First we completely classify them as a connected sum of primes webs. We also provide a m…
Graph auto-encoder predicts user-item interactions from graph data.
problem Matrix completion for recommender systems from graph data.
method Differentiable message passing on bipartite graphs.
result Competitive performance on collaborative filtering benchmarks.
Proposes new embeddings for bipartite graphs to better capture indirect relationships.
problem Typical graph embeddings fail to capture type-specific features in bipartite graphs.
method Develops two types of embeddings (FOBE and HOBE) that decompose edges into indirect relationships and uses algebraic distance for higher-order sampling.
result Ensemble embeddings improve performance over individual methods in link prediction and recommendation tasks.
Method proves complex homeomorphic to a sphere using bisimplices.
problem Proving regular CW complexes homeomorphic to spheres.
method Discrete Morse theory and bisimplices.
result Flag bisimplicial completion of quadric complexes is contractible.
Improved model for grouping nodes in bipartite networks.
problem Challenges in grouping nodes in bipartite graphs.
method Introduced DC-LBM and developed variational EM algorithm.
result Significantly enhanced performance on real-world data.
Neural execution solves complex graph problems like bipartite matching.
problem Solving complex graph algorithms like maximum bipartite matching.
method Reduces bipartite matching to a flow problem and uses Ford-Fulkerson for maximum flow.
result Neural network achieves optimal matching almost 100% of the time.
We determine for which n, the complete bipartite graph Kn,n has an embedding in S3 whose topological symmetry group is isomorphic to one of the polyhedral groups: A4, A5, or S4.
Quantum model for knotted graphs from knot theory.
problem Constructing an isotopy invariant polynomial for knotted bipartite ribbon graphs.
method Applying quantum topology to construct an isotopy invariant polynomial.
result Computed the expected number of loops in the double dimer model.
Graph neural networks speed up nonnegative matrix factorization.
problem Efficiently factorize nonnegative matrices for various applications.
method Developed a graph neural network that combines bipartite self-attention with ADMM updates.
result Significant acceleration achieved in nonnegative matrix factorization.
PAC learning simplified as bipartite matching.
problem Efficiently solving PAC learning problems.
method Transductive learning and one-inclusion graphs.
result PAC learning can be reduced to bipartite matching.
Paper uses bipartite graph to forecast cross-market returns, revealing asymmetry.
problem Cross-market return predictability and asymmetry between U.S. and Chinese markets.
method Directed bipartite graph capturing time-ordered linkages, hypothesis testing for edge selection, regularized and ensemble machine learning models.
result U.S. returns predict Chinese intraday returns, but not vice versa, revealing asymmetry.
New method embeds bipartite graphs into vectors, overcoming nonlinear challenges.
problem Learning vector representations for bipartite graphs with nonparametric components.
method Semiparametric exponential family distribution, pseudo-likelihood objective, gradient descent.
result Gradient descent achieves linear convergence rate and robust to model misspecification.
Better spectral partitioning of signed graphs using standard Laplacian.
problem Meaningless partitioning using signed Laplacian eigenvectors.
method Use standard graph Laplacian for spectral partitioning.
result Fiedler vector of standard Laplacian is easier to compute and more beneficial.
Formula for sl2 weight system on complete bipartite graphs.
problem Computing values of sl2 weight system for chord diagrams. method Chmutov-Varchenko recurrence relation, Hopf algebra projections.
result Computed values for chord diagrams with complete bipartite intersection graphs.
We study the Seifert surfaces of a link by relating the embeddings of graphs by using induced graphs. As applications, we prove that every link L is the boundary of an oriented surface which is obtained from a graph embedding of a complete bipartite graph K2,n, where all voltage assignments on the edges of $K_{2…
Let G be a connected bipartite graph with color classes E and V and root polytope Q. Regarding the hypergraph (V,E) induced by G, we prove that its interior polynomial is equivalent to the Ehrhart polynomial of Q, which in turn is equivalent to the h-vector of any triangulation of Q. It follows that the interior polyno…
This paper improves upper bounds on ribbonlength for certain alternating links.
problem Finding tighter bounds on the ribbonlength of alternating links.
method Proved a new upper bound for alternating links with bipartite dual graphs.
result Improved upper bounds on ribbonlength for specific links.
Model for operational risk using bipartite graphs and heavy-tailed distributions.
problem Capturing event type and business line structure in operational risk data.
method Statistical model based on heavy-tailed distributions and bipartite graphs.
result Reliable estimates of tail risk and capital allocations with small data sets.
Estimates treatment effects in bipartite systems with partial eligibility and interference.
problem Randomized experiments in bipartite systems with partial treatment eligibility and interference.
method Formalizes eligibility-constrained bipartite experiments, defines PTTE and STTE, identifies conditions, develops ensemble estimators, introduces projection.
result Proposed estimators recover PTTE and STTE with low bias and variance, corrects interference bias in field experiments.
New model for detecting communities in weighted bipartite networks.
problem Lack of models for weighted bipartite networks.
method Introducing Bipartite Distribution-Free model and its extension.
result Spectral algorithms for consistent estimation of node labels.
Estimates graph curvature and diameter using Laplacian eigenvalues.
problem Estimating graph curvature and diameter using Laplacian eigenvalues.
method Combination of gradient estimates and strong nodal domain walks.
result Li-Yau type eigenvalue-diameter estimate for signed graphs.