Related papers: Meta-theorems for Graph Polynomials
Meta-kernelization theorems are general results that provide polynomial kernels for large classes of parameterized problems. The known meta-kernelization theorems, in particular the results of Bodlaender et al. (FOCS'09) and of Fomin et al.…
Although some work has been done on the metamathematics of Metamath, there has not been a clear definition of a model for a Metamath formal system. We define the collection of models of an arbitrary Metamath formal system, both for…
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
The Fundamental Morphism Theorem is a categorical version of the First Noether Isomorphism Theorem for categories that do not have kernels or cokernels. We consider two categories of graphs. Both categories will admit graphs with multiple…
In this article we are introducing combinatorial spectra of graphs, this is a generalization of $H$-Hamiltonian spectra. The main motivation was to made from $H$-Hamiltonian spectra an operation and develop some algebra in this field. An…
Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs make use of the…
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
The purpose of this paper is to extend the scope of the Ehrhart theory to periodic graphs. We give sufficient conditions for the growth sequences of periodic graphs to be a quasi-polynomial and to satisfy the reciprocity laws. Furthermore,…
We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a field $k(\!(G)\!)$ of generalised power series, exploiting our…
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
This extended abstract introduces a class of graph learning applicable to cases where the underlying graph has polytopic uncertainty, i.e., the graph is not exactly known, but its parameters or properties vary within a known range. By…
The number of homomorphisms from a finite graph $F$ to the complete graph $K_n$ is the evaluation of the chromatic polynomial of $F$ at $n$. Suitably scaled, this is the Tutte polynomial evaluation $T(F;1-n,0)$ and an invariant of the cycle…
The implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined…
In this paper we define two infinite families of graphs called C-$\delta$ graphs and $\delta$- graph and prove that $\delta$-graphs satisfy $\delta$ conjecture. Also we introduce a family of C-$\delta$ graphs from which we can identify…
We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…
We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…
Isomorphisms allow human cognition to transcribe a potentially unsolvable problem from one domain to a different domain where the problem might be more easily addressed. Current approaches only focus on transcribing structural information…
In a recent paper, we studied the interaction between the automorphism group of a graph and its Tutte polynomial. More precisely, we proved that certain symmetries of graphs are clearly reflected by their Tutte polynomials. The purpose of…
In this survey of graph polynomials, we emphasize the Tutte polynomial and a selection of closely related graph polynomials. We explore some of the Tutte polynomial's many properties and applications and we use the Tutte polynomial to…