Related papers: Convex Hulls for Graphs of Quadratic Functions Wit…

We introduce a method for analyzing the convex hull of a set in non-positively curved piecewise Euclidean polygonal complexes and we apply this method to prove that, with the usual action of Fm x Zn on the metric product of the Cayley graph…

We introduce a characterization for split graphs by using edge contraction. Then, we use it to prove that any ($2K_{2}$, claw)-free graph with $\alpha(G) \geq 3$ is a split graph. Also, we apply it to characterize any pseudo-split graph.…

Let $\P$ be any collection of paths of a graph $G=(V,E)$. For $S\subseteq V$, define $I(S)=S\cup\{v\mid v \ \mbox{lies in a path of} \ \P \ \mbox{with endpoints in} \ S\}$. Let $\C$ be the collection of fixed points of the function $I$,…

A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular covers in which this locally bijective homomorphism is prescribed by an action of a subgroup of ${\rm Aut}(G)$. Regular…

In this paper, we present convex hull formulations for a mixed-integer, multilinear term/function (MIMF) that features products of multiple continuous and binary variables. We develop two equivalent convex relaxations of an MIMF and study…

We show that if the graph of a bounded analytic function in the unit disk $\mathbb D$ is not complete pluripolar in $\mathbb C^2$ then the projection of the closure of its pluripolar hull contains a fine neighborhood of a point $p \in…

We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different…

We consider a Gaussian field $X = \{X_t, t \in T\}$ with values in a Banach space $B$ defined on a parametric set $T$ equal to $R^m$ or $Z^m.$ It is supposed that the distribution $\cal P$ of $X_t$ is independent of $t.$ We consider the…

For a finite group $G$ with a normal subgroup $H$, the enhanced quotient graph of $G/H$, denoted by $\mathcal{G}_{H}(G),$ is the graph with vertex set $V=(G\backslash H)\cup \{e\}$ and two vertices $x$ and $y$ are edge connected if $xH =…

It is well known that the convex hull of $\{(x,y,xy)\}$, where $(x,y)$ is constrained to lie in a box, is given by the Reformulation-Linearization Technique (RLT) constraints. Belotti {\em et al.\,}(2010) and Miller {\em et al.\,}(2011)…

Let $G$ be a simple graph and let $S$ be a subset of its vertices. We say that $S$ is $P_3$-convex if every vertex $v \in V(G)$ that has at least two neighbors in $S$ also belongs to $S$. The $P_3$-hull set of $S$ is the smallest…

We show that for a certain class of convex functions $f$, including the exponential functions $x\mapsto e^{\lambda x}$ with $\lambda>0$ a real number, and all the powers $x\mapsto x^\beta$, $x\geq 0$ and $\beta\geq 2$ a real number, with a…

Contraction of triangles is a standard operation in the study of cubic graphs, as it reduces the order of the graph while typically preserving many of its properties. In this paper, we investigate the converse problem, wherein certain…

With the goal of obtaining strong relaxations for binary polynomial optimization problems, we introduce the pseudo-Boolean polytope defined as the convex hull of the set of binary points satisfying a collection of equations containing…

Computing the closed convex envelope or biconjugate is the core operation that bridges the domain of nonconvex with convex analysis. We focus here on computing the conjugate of a bivariate piecewise quadratic function defined over a…

In various contexts, the zeta function of an object splits into a product of $L$-functions. We categorify this product formula for quadratic covers of objects in the following contexts: quadratic extensions of number fields, ramified double…

We prove lower bounds for the fraction of edges of an $r$-graph which can be covered by the union of $k$ 1-factors. The special case $r=3$ yields some known results for cubic graphs. Furthermore, we introduce the concept of…

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…

A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…

The {\em Kneser graph} $K(2n+k,n)$, for positive integers $n$ and $k$, is the graph $G=(V,E)$ such that $V=\{S\subseteq\{1,\ldots,2n+k\} : |S|=n\}$ and there is an edge $uv\in E$ whenever $u\cap v=\emptyset$. Kneser graphs have a nice…