A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper finds minimum Dehn colors for knots and defines useful graphs for coloring.
Paper describes a state sum formula for a graph coloring polynomial.
We show that the edges of every 3-connected planar graph except can be colored with two colors in such a way that the graph has no color preserving automorphisms. Also, we characterize all graphs which have the property that their edges can be -colored so that no matter how the graph is embedded in any orienta…
The paper classifies palettes of Dehn colorings for spatial graphs.
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications and, however, are computationally difficult. In this work, a general population-b…
New TQFT homologies help color graphs, potentially solving the four color theorem.
New polynomial for checkerboard-colorable 4-valent virtual graphs.
Classifies colored links and spatial graphs up to colored link-homotopy.
Register allocation, which is a crucial phase of a good optimizing compiler, relies on graph coloring. Hence, an efficient graph coloring algorithm is of paramount importance. In this work we try to learn a good heuristic for coloring interference graphs that are used in the register allocation phase. We aim to handle …
New invariants distinguish spatial graphs not previously possible.
Uniform Lie algebras are combinatorially defined two-step nilpotent Lie algebras which can be used to define Einstein solvmanifolds. These Einstein spaces often have nontrivial isotropy groups. We derive basic properties of uniform Lie algebras and we classify uniform Lie algebras with five or fewer generators. We defi…
Graph coloring is explained using a topological field theory with defects.
Paper extends Enami-Ozeki-Yamaguchi's work on planar quadrangulations.
Invariants for trivalent graphs using algebraic colorings.
The Penrose-Kauffman polynomial connects knot theory to graph coloring.
In this article we describe a canonical way to expand a certain kind of -colored regular graphs into closed -manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial -manifold can be obtained in this way. When , we give simple eq…
This paper discusses reformulations of the problem of coloring plane maps with four colors. We give a number of alternate ways to formulate the coloring problem including a tautological expansion similar to the Penrose Bracket, and an extension of the Penrose Bracket that counts colorings of arbitrary cubic graphs pres…
The paper introduces a quantum state system to count perfect matchings in graphs.
We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lovasz. The class comprises examples of Stiefel manifolds, series of spheres and products of spheres, cubical surfaces, as well as examples of Seifert manifolds. Asymptotically, graph coloring manifolds provide examples of…
New method calculates bridge indices of spatial graphs using diagram colorings and Wirtinger number.
A {\em balanced} spatial graph has an integer weight on each edge, so that the directed sum of the weights at each vertex is zero. We describe the Alexander module and polynomial for balanced spatial graphs (originally due to Kinoshita \cite{ki}), and examine their behavior under some common operations on the graph. We…
Moduli space linked to Tait colorings of planar graphs.
The topological Tverberg theorem has been generalized in several directions by setting extra restrictions on the Tverberg partitions. Restricted Tverberg partitions, defined by the idea that certain points cannot be in the same part, are encoded with graphs. When two points are adjacent in the graph, they are not in th…
This paper consists of three parts. First, we generalize the Jaeger Formula to express the Kauffman-Vogel graph polynomial as a state sum of the Murakami-Ohtsuki-Yamada graph polynomial. Then, we demonstrate that reversing the orientation and the color of a MOY graph along a simple circuit does not change the sl(N) Mur…
Kronheimer-Mrowka's instanton homology dimension equals Tait colorings.
The paper finds 3-colorings of 2-sphere triangulations.
A colored graph is a directed graph in which nodes or edges have been assigned colors that are not necessarily unique. Observability problems in such graphs consider whether an agent observing the colors of edges or nodes traversed on a path in the graph can determine which node they are at currently or which nodes wer…
Algorithm determines spatial graph isomorphism with vertex, edge colorings and orientations.
The Kauffman-Vogel polynomials are three variable polynomial invariants of -valent rigid vertex graphs. A one-variable specialization of the Kauffman-Vogel polynomials for unoriented -valent rigid vertex graphs was given by using the Kauffman bracket and the Jones-Wenzl idempotent colored with . Bataineh, Elha…
In this paper, we show that a simple coloring scheme can improve, both theoretically and empirically, the expressive power of Message Passing Neural Networks(MPNNs). More specifically, we introduce a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate identical node att…
Graph potentials link to topological QFTs, with computational methods.
Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual…
Murakami-Ohtsuki-Yamada introduced an evaluation of certain oriented planar trivalent graphs with colored edges. This evaluation plays a key role in the evaluation of the colored HOMFLY polynomial of a link in 3-space and its Khovanov-Rozansky categorification. Our goal is is to give a generating series formula for the…
Fox coloring provides a combinatorial framework for studying dihedral representations of the knot group. The less well-known concept of Dehn coloring captures the same data. Recent work of Carter-Silver-Williams clarifies the relationship between the two focusing on how one transitions between Fox and Dehn colorings. I…
Consider the collection of edge bicolorings of a graph that is cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and reversing colors around a vertex. In the case of the plane, this is well studied…
A representation for compact 3-manifolds with non-empty non-spherical boundary via 4-colored graphs (i.e., 4-regular graphs endowed with a proper edge-coloration with four colors) has been recently introduced by two of the authors, and an initial classification of such manifolds has been obtained up to 8 vertices of th…
SON-GOKU uses graph coloring to improve multi-task learning by partitioning tasks into compatible groups.
Every cubic graph is a bridge trisection's 1-skeleton for a knotted surface.
Let N be a regular branched cover of a homology 3-sphere M with deck group G isomorphic to Z_2^d and branch set a trivalent graph Gamma; such a cover is determined by a coloring of the edges of Gamma with elements of G. For each index-2 subgroup H of G, M_H = N/H is a double branched cover of M. Sakuma has proved that …
In-degree quiver polynomials for surface-links computed.
The space C of conservative vertex colorings (over a field F) of a countable, locally finite graph G is introduced. The subspace of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Z^d-action by automorphisms, C is a finitely generated module over the polynomial ring…
We present a new notion of probabilistic duality for random variables involving mixture distributions. Using this notion, we show how to implement a highly-parallelizable Gibbs sampler for weakly coupled discrete pairwise graphical models with strictly positive factors that requires almost no preprocessing and is easy …
We introduce a representation via (n+1)-colored graphs of compact n-manifolds with (possibly empty) boundary, which appears to be very convenient for computer aided study and tabulation. Our construction is ageneralization to arbitrary dimension of the one recently given by Cristofori and Mulazzani in dimension three, …
The G-degree of colored graphs is a key concept in the approach to Quantum Gravity via tensor models. The present paper studies the properties of the G-degree for the large class of graphs representing singular manifolds (including closed PL manifolds). In particular, the complete topological classification up to G-deg…
The paper computes groups and modules for wheel graphs using Fibonacci and Chebyshev polynomials.
The contents of this 98-page paper have been subsumed into the 191-page paper "A colored sl(N)-homology for links in S^3" (arXiv:0907.0695v1 [math.GT]), in which we further develop the theory and use it to construct a colored link homology.
We define a functor from the category of multiple conjugation biquandles to that of multiple conjugation quandles. We show that for any multiple conjugation biquandle , there is a one-to-one correspondence between the set of -colorings and that of -colorings diagrammatically for any …
We introduce colorings of oriented surface-links by biquasiles using marked graph diagrams. We use these colorings to define counting invariants and Boltzmann enhancements of the biquasile counting invariants for oriented surface-links. We provide examples to show that the invariants can distinguish both closed surface…