Results 51 to 60 of about 3,648 (134)
Discrete & Computational GeometryAbstract We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by Berget, Eur, Spink and Tseng to the product space $${{\mathbb {P}}}^n \times {{\mathbb {P}}}^n$$
Mario Bauer +4 more
openaire +2 more sources
A tropical approach to rigidity: Counting realisations of frameworks
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A realisation of a graph in the plane as a bar‐joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely many realisations can be seen as a solution to a system of quadratic equations prescribing the distances between pairs of points.
Oliver Clarke +6 more
wiley +1 more source
Tutte and Jones polynomials of link families
, 2010 This article contains general formulas for Tutte and Jones polynomials for families of knots and links given in Conway notation and "portraits of families"-- plots of zeroes of their corresponding Jones ...
Jablan, Slavik +2 more
core +1 more source
Crossing estimates for the Ising model on general s‐embeddings
Proceedings of the London Mathematical Society, Volume 131, Issue 4, October 2025.Abstract We prove Russo–Seymour–Welsh‐type crossing estimates for the FK–Ising model on general s‐embeddings whose origami map has an asymptotic Lipschitz constant strictly smaller than 1, provided it satisfies a mild non‐degeneracy assumption. This result extends the work of Chelkak and provides a general framework to prove that the usual connection ...
Rémy Mahfouf
wiley +1 more source
A Sharper Ramsey Theorem for Constrained Drawings
Journal of Graph Theory, Volume 109, Issue 4, Page 401-411, August 2025.ABSTRACT Given a graph G and a collection C of subsets of R d indexed by the subsets of vertices of G, a constrained drawing of G is a drawing where each edge is drawn inside some set from C, in such a way that nonadjacent edges are drawn in sets with disjoint indices. In this paper we prove a Ramsey‐type result for such drawings.
Pavel Paták
wiley +1 more source
Basilica: New canonical decomposition in matching theory
Journal of Graph Theory, Volume 108, Issue 3, Page 508-542, March 2025.Abstract In matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are ...
Nanao Kita
wiley +1 more source
Combinatorics, Probability and Computing, 2018 We follow the example of Tutte in his construction of the dichromate of a graph (i.e. the Tutte polynomial) as a unification of the chromatic polynomial and the flow polynomial in order to construct a new polynomial invariant of maps (graphs embedded in orientable surfaces). We call this the surface Tutte polynomial.
Vena, Lluis +4 more
openaire +6 more sources
On finite generation in magnitude (co)homology and its torsion
Bulletin of the London Mathematical Society, Volume 56, Issue 11, Page 3434-3451, November 2024.Abstract The aim of this paper is to apply the framework developed by Sam and Snowden to study structural properties of graph homologies, in the spirit of Ramos, Miyata and Proudfoot. Our main results concern the magnitude homology of graphs introduced by Hepworth and Willerton, and we prove that it is a finitely generated functor (on graphs of bounded
Luigi Caputi, Carlo Collari
wiley +1 more source
Discrete Mathematics, 2001 The authors look at the Tutte polynomials of \(q\)-cones \((q\)-lifts) of combinatorial geometries (simple matroids) representable over \(\text{GF}(q)\). A formula is derived for the Tutte polynomial of all \(q\)-cones of \(G\) in terms of the Tutte polynomial of \(G\).
E. Bonin, Joseph, Qin, Hongxun
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The scaling limit of random cubic planar graphs
Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.Abstract We study the random cubic planar graph Cn$\mathsf {C}_n$ with an even number n$n$ of vertices. We show that the Brownian map arises as Gromov–Hausdorff–Prokhorov scaling limit of Cn$\mathsf {C}_n$ as n∈2N$n \in 2 \mathbb {N}$ tends to infinity, after rescaling distances by γn−1/4$\gamma n^{-1/4}$ for a specific constant γ>0$\gamma >0$. This is
Benedikt Stufler
wiley +1 more source