Related papers: Strongly sublinear separators and polynomial expan…
We say a polynomial f having integer coefficients is strongly coefficient convex if the set of coefficients of f consists of consecutive integers only. We establish various results suggesting that the divisors of x^n-1 with integer…
This paper considers a hyperplane arrangement constructed with a subset of a set of all simple paths in a graph. A connection of the constructed arrangement to the maximum matching problem is established. Moreover, the problem of finding…
We characterize a large subclass of the class of those graphs $G$ for which the exponential domination number of $H$ equals the domination number of $H$ for every induced subgraph $H$ of $G$.
A directed graph $G=(V,E)$ is {\it strongly pseudo transitive} if there is a partition $\{A,E-A\}$ of $E$ so that graphs $G_1=(V,A)$ and $G_2=(V,E-A)$ are transitive, and additionally, if $ab\in A$ and $bc\in E $ implies that $ac\in E$. A…
This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential…
We show that, in general, the characteristic polynomial of a hypergraph is not determined by its ``polynomial deck'', the multiset of characteristic polynomials of its vertex-deleted subgraphs, thus settling the ``polynomial reconstruction…
Let G be a simple graph of order n. The domination polynomial of a graph is the generating function of its dominating sets. We study the domination polynomials of generalized friendship graphs. We also consider book graphs formed by joining…
It is known that non-isomorphic strongly regular graphs with the same parameters must be cospectral (have the same eigenvalues). In this paper, we investigate whether the spectra of higher order Laplacians associated with these graphs can…
Dallard, Milani\v{c}, and \v{S}torgel conjectured that for a hereditary graph class $\mathcal{G}$, if there is some function $f:\mathbb{N}\to\mathbb{N}$ such that every graph $G\in \mathcal{G}$ with clique number $\omega(G)$ has treewidth…
The greedy spanner in a low dimensional Euclidean space is a fundamental geometric construction that has been extensively studied over three decades as it possesses the two most basic properties of a good spanner: constant maximum degree…
We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank…
For a hereditary class C of graphs, let s_C(n) be the minimum function such that each n-vertex graph in C has a balanced separator of order at most s_C(n), and let nabla_C(r) be the minimum function bounding the expansion of C, in the sense…
We give a new characterization of the vertical-strip LLT polynomials $\mathrm{LLT}_P(x;q)$ as the unique family of symmetric functions that satisfy certain combinatorial relations. This characterization is then used to prove an explicit…
As an application of Szemeredi's regularity lemma, Erdos-Frankl-Rodl (1986) showed that the number of graphs on vertex set {1,2,...n} with a monotone class P is $2^{(1+o(1))ex(n,P)n^2/2}$ where $ex(n,P)$ is the maximum number of edges of an…
We study a class of polynomials that has all of its roots on the critical line and shares many properties with Ehrhart polynomials. Braun showed that the roots of Ehrhart polynomials are bounded quadratically and Higashitani provided…
We introduce a new one-variable polynomial invariant of graphs, which we call the skew characteristic polynomial. For an oriented simple graph, this is just the characteristic polynomial of its anti-symmetric adjacency matrix. For…
Let G = (V;E) be a simple graph. We consider domination polynomial, matching polynomial and edge cover polynomial of G. Graphs which their polynomials have few roots can give sometimes a very surprising information about the structure of…
We study types that appear in ultraproducts that have distributions which can be thought of as a sequence of graphs. The property of having distributions that are captured by graphs is motivated by a commonality of $\mathrm{SOP}_2$-types…
We build an explicit link between coherent functors in the sense of Auslander and strict polynomial functors in the sense of Friedlander and Suslin. Applications to functor cohomology are discussed.
In this note we give a short proof that graphs having no linearly small F{\o}lner sets can be partitioned into a union of expanders. We use this fact to prove a partition result for graphs admitting linearly small maximal F{\o}lner sets and…