Related papers: A proof of Pieri's formula using the generalized S…
A graph is $k$-degenerate if any induced subgraph has a vertex of degree at most $k$. In this paper we prove new algorithms for cliques and similar structures for these graphs. We design linear time Fixed-Parameter Tractable algorithms for…
In a recent paper by the authors, a new approach--called the "embedding method"--was introduced, which allows to make use of exchangeable pairs for normal and multivariate normal approximation with Stein's method in cases where the…
We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.
We provide a graphical calculus for computing averages of tensor network diagrams with respect to the distribution of random vectors containing independent uniform complex phases. Our method exploits the order structure of the partially…
Recent years are characterized by an unprecedented quantity of available network data which are produced at an astonishing rate by an heterogeneous variety of interconnected sensors and devices. This high-throughput generation calls for the…
Estimating the average degree of graph is a classic problem in sublinear graph algorithm. Eden, Ron, and Seshadhri (ICALP 2017, SIDMA 2019) gave a simple algorithm for this problem whose running time depended on the graph arboricity, but…
As a generalization of Hermite interpolation problem, Birkhoff interpolation is an important subject in numerical approximation. This paper generalizes the existing Generalized Recursive Polynomial Interpolation Algorithm (GRPIA) that is…
Consider a finite directed graph without cycles in which the arrows are weighted. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context…
We investigate generalizations of pebbling numbers and of Graham's pebbling conjecture that pi(GxH) <= pi(G)pi(H), where pi(G) is the pebbling number of the graph G. We develop new machinery to attack the conjecture, which is now twenty…
We present an elementary proof of a generalization of Kirchoff's matrix tree theorem to directed, weighted graphs. The proof is based on a specific factorization of the Laplacian matrices associated to the graphs, which only involves the…
Let $H$, $T$ and $C_n$ be a graph, a tree and a cycle of order $n$, respectively. Let $H^{(i)}$ be the complete join of $H$ and an empty graph on $i$ vertices. Then the Cartesian product $H\Box T$ of $H$ and $T$ can be obtained by applying…
We review the theory of Cheeger constants for graphs and quantum graphs and their present and envisaged applications.
We produce Brill-Noether general graphs in every genus, confirming a conjecture of Baker and giving a new proof of the Brill-Noether Theorem, due to Griffiths and Harris, over any algebraically closed field.
In this paper we present a new Good Characterization of maximum genus of a graph which makes a common generalization of the works of Xuong, Liu, and Fu et al. Based on this, we find a new polynomially bounded algorithm to find the maximum…
We introduce a novel framework for graph signal processing (GSP) that models signals as graph distribution-valued signals (GDSs), which are probability distributions in the Wasserstein space. This approach overcomes key limitations of…
There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial "refinement" algorithms seem to be very efficient in practice. Some philosophical justification is provided by a classical theorem of…
Given n data points in R^d, an appropriate edge-weighted graph connecting the data points finds application in solving clustering, classification, and regresssion problems. The graph proposed by Daitch, Kelner and Spielman (ICML~2009) can…
A new formula for the probability that a standard Brownian motion stays between two linear boundaries is proved. A simple algorithm is deduced. Uniform precision estimates are computed. Different implementations have been made available…
We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…
Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.