Related papers: On $k$-Connected $\Gamma$-Extensions of Binary Mat…
We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an expanding subgraph of G. Our results imply that if one of these…
The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$ was introduced by Chartrand et al. in 1984. It is natural to introduce the concept of generalized $k$-edge-connectivity $\lambda_k(G)$. For general $k$, the generalized…
The $es$-splitting operation on binary bridge-less matroids never produces an Eulerian matroid. But for matroids representable over $GF(p),(p>2),$ called $p$-matroids, the $es$-splitting operation may yield Eulerian matroids. In this work,…
We introduce the \Gamma-extension of the spectrum of the Laplacian of a Riemannian orbifold, where \Gamma is a finitely generated discrete group. This extension, called the \Gamma-spectrum, is the union of the Laplace spectra of the…
Many variants of join operations of graphs have been introduced and their spectral properties have been studied extensively by many researchers. This paper mainly focuses on the Laplacian spectra of some double join operations of graphs. We…
We prove that the extension complexity of the independence polytope of every regular matroid on $n$ elements is $O(n^6)$. Past results of Wong and Martin on extended formulations of the spanning tree polytope of a graph imply a $O(n^2)$…
An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of…
Binary idempotent semirings govern classical path algebras. Their multiplicative structure is dyadic. We examine whether this restriction is structural or accidental. We define ternary idempotent $\Gamma$-semirings as higher-arity ordered…
We study the closure operators of polymatroids from a lattice theoretic point of view. We show that polymatroid closure operators relate to lattices enriched with a generating set in the same way that matroids relate to geometric lattices.…
There has been wide interest in understanding which properties of base graphs of matroids extend to base-cobase graphs of matroids. A significant result of Naddef and Pulleyblank (1984) shows that the $1$-skeleton of any $(0,1)$-polytope is…
We use planar 4-valent graphs and a graphical calculus involving such graphs to construct an invariant for balanced-oriented, knotted 4-valent graphs. Our invariant is an extension of the $sl(n)$ polynomial for classical knots and links. We…
L. Lovasz has shown that Sperner's combinatorial lemma admits a generalization involving a matroid defined on the set of vertices of the associated triangulation. Inspired by this result we prove that classical Ky Fan's theorem admits an…
Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…
Back in the Eighties, Heath showed that every 3-planar graph is subhamiltonian and asked whether this result can be extended to a class of graphs of degree greater than three. In this paper we affirmatively answer this question for the…
The paper considers a Clifford extension of the Grassmann algebra, in which operators are built from Grassmann variables and by the derivatives with respect to them. It is shown that a subalgebra which is isomorphic to the usual matrix…
The stable mod 2 cohomologies of the spectra for connective real and complex K-theories are well known and easy to work with. However, the known bases are in terms of the anti-automorphism of Milnor basis elements. We offer simple bases in…
An oriented graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathsf{B}$ with nonnegative structure constants in which the matrix of the multiplication by $A$ coincides with…
In this paper, we give a complete characterization of binary matroids with no $P_9$-minor. A 3-connected binary matroid $M$ has no $P_9$-minor if and only if $M$ is one of the internally 4-connected non-regular minors of a special…
In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be…
A tract $F$ is an algebraic structure where multiplication is defined but addition is only partially defined. They were introduced by Baker and Bowler as a unified framework to study generalisations of matroids, including oriented and…