Related papers: Graph-different permutations
We compute the whole asymptotic expansion of the probability that a large uniform labeled graph is connected, and of the probability that a large uniform labeled tournament is irreducible. In both cases, we provide a combinatorial…
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…
Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…
We show that a nontrivial graph isomorphism problem of two undirected graphs, and more generally, the permutation similarity of two given $n\times n$ matrices, is equivalent to equalities of volumes of the induced three convex bounded…
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very…
Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…
We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such…
Bidirected graphs are multigraphs where every edge has an independent direction at each end. In the paper, with an arbitrary bidirected graph we associate a non-negative integral quadratic form (called the incidence form of the graph), and…
It is shown that shift graphs can be realized as disjointness graphs of 1-intersecting curves in the plane. This implies that the latter class of graphs is not $\chi$-bounded.
We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed…
The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…
This paper presents a new graph isomorphism invariant, called $\mathfrak{w}$-labeling, that can be used to design a polynomial-time algorithm for solving the graph isomorphism problem for various graph classes. For example, all…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
In a graph, we assign distinct integers to the vertices, and take the sum of two integers if they are on two adjacent vertices. The minimum possible number of different sums is the \emph{sum index} of this graph. In this paper, we present…
Generative models of graph structure have applications in biology and social sciences. The state of the art is GraphRNN, which decomposes the graph generation process into a series of sequential steps. While effective for modest sizes, it…
We find the asymptotic number of connected graphs with $k$ vertices and $k-1+l$ edges when $k,l$ approach infinity, reproving a result of Bender, Canfield and McKay. We use the {\em probabilistic method}, analyzing breadth-first search on…
In 2019, investigation of the so-called factor-invariant cubic graphs was initiated by Alspach, Khodadadpour and Kreher. For a cubic graph $\Gamma$ and a vertex-transitive subgroup $G$ of $\mathrm{Aut}(\Gamma)$, a $2$-factor $\mathcal{C}$…
A new approach to find all the transitive orientations for a comparability graph (finite or infinite) is presented. This approach is based on the link between the notion of ``strong'' partitive set and the forcing theory (notions of…
We introduce a family of adaptive estimators on graphs, based on penalizing the $\ell_1$ norm of discrete graph differences. This generalizes the idea of trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate…
The asymptotic study of percolation on finite transitive graphs is considered. Several questions and very few answers regarding percolation on finite graphs are presented.