Related papers: A graph theoretic proof of Cramer's rule

We expose here a short proof of Cramer's theorem in R based on convex duality.

In this note, we introduce a new method for constructing graphs with high chromatic number and small clique. Indeed, via this method, we present a new proof for the well-known Kneser's conjecture.

We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…

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

In view of Tucker's lemma (an equivalent combinatorial version of the Borsuk- Ulam theorem), the present authors (2013) introduced the kth altermatic number of a graph G as a tight lower bound for the chromatic number of G. In this note, we…

We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.

We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from labelled graphs.

In this paper we present a combinatorial proof of Selberg's integral formula. We start by giving a bijective proof of a Theorem about the number of topological orders of a certain related directed graph. Selberg's Integral Formula then…

We present new combinatorial insights into the calculation of (Castelnuovo-Mumford) regularity of graphs.

We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of $n$-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the…

We investigate combinatorial properties of a graph polynomial indexed by half-edges of a graph which was introduced recently to understand the connection between Feynman rules for scalar field theory and Feynman rules for gauge theory. We…

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

A proof of Sharkovsky's Theorem is given. It is shown how this proof naturally generalizes to looking at maps on graphs and to Sharkovsky-type theorems for these maps. The paper is written at an elementary level and is meant as an…

In this note we propose an $\omega$-operadical way to prove the existence of the $\omega$-graph of the $\omega$-graphs and the reflexive $\omega$- graph of the reflexive $\omega$-graphs.

This work considers new entropy-based proofs of some known, or otherwise refined, combinatorial bounds for bipartite graphs. These include upper bounds on the number of the independent sets, lower bounds on the minimal number of colors in…

The proof of Brouwer's fixed-point theorem based on Sperner's lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial…

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

We introduce a notion of curvature on finite, combinatorial graphs. It can be easily computed by solving a linear system of equations. We show that graphs with curvature bounded below by $K>0$ have diameter bounded by $\mbox{diam}(G) \leq…

We prove a combinatorial lemma about the distribution of directed currents in a complex "loop soup" and use it to give a new proof of the isomorphism relating loop measures and complex Gaussian fields.

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.