Results 51 to 60 of about 495 (157)

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

On the polymatroid Tutte polynomial

Journal of Combinatorial Theory, Series A
The Tutte polynomial is a well-studied invariant of matroids. The polymatroid Tutte polynomial $\mathcal{J}_{P}(x,y)$, introduced by Bernardi et al., is an extension of the classical Tutte polynomial from matroids to polymatroids $P$. In this paper, we first prove that $\mathcal{J}_{P}(x,t)$ and $\mathcal{J}_{P}(t,y)$ are interpolating for any fixed ...
Xiaxia Guan, Weiling Yang, Xian'an Jin
openaire   +3 more sources

Tutte polynomials of q-cones

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 \(G\).
Joseph E. Bonin, Hongxun Qin
openaire   +2 more sources

The multivariate arithmetic Tutte polynomial [PDF]

Transactions of the American Mathematical Society, 2012
We introduce an arithmetic version of the multivariate Tutte polynomial and a quasi-polynomial that interpolates between the two. A generalized Fortuin-Kasteleyn representation with applications to arithmetic colorings and flows is obtained. We give a new and more general proof of the positivity of the coefficients of the arithmetic Tutte polynomial ...
Branden P, Moci L
openaire   +7 more sources

Data from "Simulating Quantum Computations with Tutte Polynomials"

, 2021
Source code and experimental data for the paper "Simulating Quantum Computations with Tutte Polynomials" by Ryan L ...
Montanaro, Ashley, Mann, Ryan
core   +1 more source

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

On coefficients of the Tutte polynomial

Discrete Mathematics, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

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

Computing the Tutte Polynomial of hyperplane arrangements [PDF]

, 2009
textWe are studying the Tutte Polynomial of hyperplane arrangements. We discuss some previous work done to compute these polynomials. Then we explain our method to calculate the Tutte Polynomial of some arrangements more efficiently.
Geldon, Todd Wolman
core