Let
A
A signed graph is a pair
We call an induced cycle of length at least four a hole. The parity of a hole is the parity of its length. Forbidding holes of certain types in a graph has deep structural implications. In 2006, Chudnovksy, Seymour, Robertson, and Thomas famously proved that a graph is perfect if and only if it does not contain an odd hole or a complement of an odd hole. In 2002, Conforti, Cornuéjols,...
The oriented Ramsey number
We also show that if
The list switch homomorphisms problem
The study of patterns in inversion sequences was initiated by Corteel-Martinez-Savage-Weselcouch and Mansour-Shattuck independently. This talk introduces some investigation on several classical statistics on restricted inversion sequences that are either known or conjectured to be enumerated by Catalan, Large Schröder, Baxter and Euler numbers. This talk is based on joint work with Zhicong Lin...
Bonnet, Kim, Thomass\'{e}, and Watrigant (2020) introduced the twin-width of a graph. We show that the twin-width of an
A family
Helly's theorem and its variants asserts that for a family of convex sets in Euclidean space, local intersection patterns influence global intersection patterns. A classical result of Eckhoff in 1988 provided an optimal fractional Helly theorem for axis-parallel boxes, which are Cartesian products of line segments. Answering a question raised by Barany and Kalai, and independently by Lew, we...
We study a natural generalization of the well-studied Tur\'an problems, known as multicolor Tur\'an problems, which was first introduced and nurtured by Keevash, Saks, Sudakov, and Verstra\"{e}te. A simple
We define an n-dimensional projective smooth toric variety associated with a triangulation of the (n+2)-gon. Such a toric variety is called of Catalan type. We show that toric varieties of Catalan type are Fano Bott manifolds, and they appear in certain smooth toric Richardson varieties in the flag variety. We also see that toric varieties of Catalan type are classified up to isomorphism in...
What is the largest number
A dominating set of a graph
When two balls in a metric space has small intersection? We give some natural conditions to guarantee an exponential decay on the volume of such intersections. Our proof is conceptually simple, making use of concentration of measure on a "slice". We will discuss a couple of applications of this volume estimate in coding theory. This is joint work with Jaehoon Kim and Tuan Tran.
The (manufacturer's) pallet loading problem has been a topic of wide interest for operational research and companies for more than 50 years. It is to find the optimal loading of identical rectangular boxes onto a single rectangular pallet (also allowing for 90 degree rotation).
It was already known that all box layouts in the given pallet are completely determined by the set of efficient...
This talk presents a method for detecting and restoring integer datasets that have been manipulated by operations involving non-integral real-number multiplication and rounding. Detecting and restoring such manipulated integer datasets is not straightforward, nor are there any known solutions. We introduce the manipulation process, which was motivated by an actual case of fraud on the TV...