Related papers: A Simple Proof of Sharkovsky's Theorem
In this note, we give short inductive proofs of two known results on $k$-extendible graphs based on a property proved in [Qinglin Yu, A note on $n$-extendable graphs. Journal of Graph Theory, 16:349-353, 1992].
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
We give a new simpler proof of a theorem of Jayne and Rogers.
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
We present a simpler proof of Naji's characterization of circle graphs.
A new very simple proof of the number of labeled rooted forest-graphs with a given number of vertices is given. As a partial case of this formula we have Cayley's formula.
A very short proof of Kneser's theorem via transversal is given.
We give streamlined proofs of theorems of S.\ Smirnov about the decomposition of vector fields of measures into curves.
We study Cantor's powerset theorem from a graph-theoretic perspective, consider some alternative proofs to Cantor's original, and provide a new proof.
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
In this paper, we present a short proof of Halin's grid theorem.
We present a short proof of Szemer\'edi's Theorem using a dynamical system enriched by ideas from model theory. The resulting proof contains features reminiscent of proofs based on both ergodic theory and on hypergraph regularity.
We present a streamlined and simplified proof of the Kakeya set conjecture in $\mathbb{R}^3$.
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…
This document presents a simpler proof showcasing the NP-hardness of Familial Graph Compression.
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
We present an alternative proof of Sanov's theorem for Polish spaces in the weak topology that follows via discretization arguments. We combine the simpler version of Sanov's Theorem for discrete finite spaces and well chosen finite…
We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.