Related papers: On $k$-Connected $\Gamma$-Extensions of Binary Mat…
In this paper, we deal with a generalization $\Gamma(\Omega,q)$ of the bipartite graphs $D(k,q)$ proposed by Lazebnik and Ustimenko, where $\Omega$ is a set of binary sequences that are adopted to index the entries of the vertices. A few…
Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371…
Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least $\ell$. In a previous paper by the authors, a generalization was…
This paper formulates a novel problem on graphs: find the minimal subset of edges in a fully connected graph, such that the resulting graph contains all spanning trees for a set of specifed sub-graphs. This formulation is motivated by an…
We prove two extension theorems for positive maps from operator systems into matrix algebras
Using the combinatorial species setting, we propose two new operad structures on multigraphs and on pointed oriented multigraphs. The former can be considered as a canonical operad on multigraphs, directly generalizing the…
We study a class of graph Hamiltonians given by a type of quiver representation to which we can associate (non)--commutative geometries. By selecting gauging data these geometries are realized by matrices through an explicit construction or…
We show how to find and efficiently maintain maximal k-edge-connected subgraphs in undirected graphs. In particular, we provide the following results. (1) A general framework for maintaining the maximal k-edge-connected subgraphs upon…
The classical Whitney's 2-Isomorphism Theorem describes the families of graphs having the same cycle matroid. In this paper we describe the families of graphs having the same truncated cycle matroid and prove, in particular, that every…
Frame matroids and lifted-graphic matroids are two distinct minor-closed classes of matroids, each of which generalises the class of graphic matroids. The class of quasi-graphic matroids, recently introduced by Geelen, Gerards, and Whittle,…
Let $\Gamma$ be a Cayley graph, or a Cayley sum graph, or a twisted Cayley graph, or a twisted Cayley sum graph, or a vertex-transitive graph. Suppose $\Gamma$ is undirected and non-bipartite. Let $\mu$ (resp. $\mu_2$) denote the smallest…
Let $\Gamma=\Gamma(A)$ denote a simple strongly connected digraph with vertex set $X$, diameter $D$, and let $\{A_0,A:=A_1,A_2,\ldots,A_D\}$ denote the set of distance-$i$ matrices of $\Gamma$. Let $\{R_i\}_{i=0}^D$ denote a partition of…
For $L^2$-normalized joint eigenfunctions in a quantum integrable system, [GT20] gave polynomial improvements over the standard H\"omander bounds for typical points. In this paper, we improve their result by establishing a sharp bound of…
It is known that if $n$ vertices can be removed from a connected graph $\Gamma$ so that no subgraphs isomorphic to the graph $K$ remain, then no more than $|V(K)|\cdot n$ vertices can be removed, forming a set invariant with respect to all…
We provide an optimal sufficient condition, relating minimum degree and bandwidth, for a graph to contain a spanning subdivision of the complete bipartite graph $K_{2,\ell}$. This includes the containment of Hamilton paths and cycles, and…
In this paper, we prove that the Chow ring and augmented Chow ring of a matroid are equivariantly $\gamma$-positive under the action of any group of automorphisms. Our approach provides an explicit combinatorial interpretation of the…
We say that a $d$-regular graph is a $\gamma$-expander if for every not too large set of vertices $S$, there are at least $\gamma d |S|$ edges leaving $S$, and we say that a graph $G$ is $\gamma$-far from bipartite if at least $\gamma e(G)$…
In the paper we investigate an algorithmic associative binary operation $*$ on the set $\mathcal{LR}_1$ of Littlewood-Richardson tableaux with entries equal to one. We extend $*$ to an algorithmic nonassociative binary operation on the set…
We continue our investigation of binary actions of simple groups. In this paper, we demonstrate a connection between the graph $\Gamma(\mathcal{C})$ based on the conjugacy class $\mathcal{C}$ of the group $G$, which was introduced in our…
We introduce a white graph expansion for the method of perturbative continuous unitary transformations when implemented as a linked cluster expansion. The essential idea behind an expansion in white graphs is to perform an optimized…