Related papers: Speyer's elegant topological proof for Kasteleyn's…

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

This is a recreational paper showing that certain linked graphs cannot be separated. The proofs employ elementary covering space theory, an appeal to a theorem of Scharlemann (concerning the band sums of two unknots), and a Jones polynomial…

We study Cantor's powerset theorem from a graph-theoretic perspective, consider some alternative proofs to Cantor's original, and provide a new proof.

Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…

In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.

The aim of this text is to provide an elementary and self-contained exposition of Gromov's argument on topological overlap (the presentation is based on Gromov's work, as well as two follow-up papers of Matousek and Wagner, and of…

We present in this work a new and simple proof of the false centre theorem.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

The purpose of this note is to start the systematic analysis of cofinal types of topological groups.

We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…

A conjecture regarding the structure of expander graphs is discussed.

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

The goal of this paper is to show that there exists a simple, yet universal statistical logic of spectral graph analysis by recasting it into a nonparametric function estimation problem. The prescribed viewpoint appears to be good enough to…

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

We define the notion of a twisted topological graph algebra associated to a topological graph and a $1$-cocycle on its edge set. We prove a stronger version of a Vasselli's result. We expand Katsura's results to study twisted topological…

This note is withdrawn. The result and its proof are available in the literature.

A one-line proof of a minimax theorem due to Steinerberger is given.