Related papers: A note on the structure of expanders

Recently, in the paper \cite{CJKM1} we suggested the two conjectures about the diameter of io-decomposable Riordan graphs of the Bell type. In this paper, we give a counterexample for the first conjecture. Then we prove that the first…

We propose to generalize the volume conjecture to knotted trivalent graphs and we prove the conjecture for all augmented knotted trivalent graphs. As a corollary we find that for any link L there is a link containing L for which the volume…

We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "contracted diameter less or equal to 2" condition, with minimal degree greater or equal to k, and some natural hypothesis on the edges connecting…

In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.

This is an expository paper (in Spanish) describing the origin and history of the Hirsch Conjecture about the maximum diameter of graphs of polytopes, and the ideas that led to the counter-example to it recently announced by the author in…

An algebraic deformation theory of coalgebra morphisms is constructed.

We describe a correspondence between GL_n-invariant tensors and graphs, and show how this correspondence accomodates various types of symmetries and orientations.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

Some notes and observations on analytic functions defined on an annulus

We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.

We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants…

The divisor theory for graphs is compared to the theory of linear series on curves through the correspondence associating a curve to its dual graph. An algebro-geometric interpretation of the combinatorial rank is proposed, and proved in…

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.

We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

In this paper we discuss the connected components of underlying graphs of halving lines' configurations. We show how to create a configuration whose underlying graph is the union of two given underlying graphs. We also prove that every…

A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…

We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary.

These notes are a self-contained short proof of the stability of persistence diagrams.

Expander graphs, due to their mixing properties, are useful in many algorithms and combinatorial constructions. One can produce an expander graph with high probability by taking a random graph (e.g., the union of $d$ random bijections for a…