相关论文: Generating facets for the cut polytope of a graph …
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
We investigate the problem of determining if a given graph corresponds to the dual of a triangulation of a simple polygon. This is a graph recognition problem, where in our particular case we wish to recognize a graph which corresponds to…
Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here we present an alternative method based on a combination of algebraic results on…
Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at…
We derive here the Friedland-Tverberg inequality for positive hyperbolic polynomials. This inequality is applied to give lower bounds for the number of matchings in $r$-regular bipartite graphs. It is shown that some of these bounds are…
We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…
Chordal structure and bounded treewidth allow for efficient computation in numerical linear algebra, graphical models, constraint satisfaction and many other areas. In this paper, we begin the study of how to exploit chordal structure in…
A balanced partition is a clustering of a graph into a given number of equal-sized parts. For instance, the Bisection problem asks to remove at most k edges in order to partition the vertices into two equal-sized parts. We prove that…
Given a complete simple topological graph $G$, a $k$-face generated by $G$ is the open bounded region enclosed by the edges of a non-self-intersecting $k$-cycle in $G$. Interestingly, there are complete simple topological graphs with the…
Hypergraphs have gained increasing attention in the machine learning community lately due to their superiority over graphs in capturing super-dyadic interactions among entities. In this work, we propose a novel approach for the partitioning…
A common theme in many extremal problems in graph theory is the relation between local and global properties of graphs. One of the most celebrated results of this type is the Ruzsa-Szemer\'edi triangle removal lemma, which states that if a…
Suppose we are given a bipartite graph that admits a perfect matching and an adversary may delete any edge from the graph with the intention of destroying all perfect matchings. We consider the task of adding a minimum cost edge-set to the…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
Symmetric edge polytopes of graphs are important object in Ehrhart theory,and have an application to Kuramoto models. In the present paper, we study the upper and lower bounds for the number of facets of symmetric edge polytopes of…
A fundamental task for knowledge graphs (KGs) is knowledge graph completion (KGC). It aims to predict unseen edges by learning representations for all the entities and relations in a KG. A common concern when learning representations on…
We identify a family of $O(|E(G)|^2)$ nontrivial facets of the connected matching polytope of a graph $G$, that is, the convex hull of incidence vectors of matchings in $G$ whose covered vertices induce a connected subgraph. Accompanying…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
Adversarial example is a rising way of protecting facial privacy security from deepfake modification. To prevent massive facial images from being illegally modified by various deepfake models, it is essential to design a universal deepfake…
Graph pooling has been increasingly considered for graph neural networks (GNNs) to facilitate hierarchical graph representation learning. Existing graph pooling methods commonly consist of two stages, i.e., selecting the top-ranked nodes…