相关论文: Termination orders for 3-polygraphs
We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually…
A concept of a rectangular diagram of a foliation in the three-sphere is introduced. It is shown that any co-orientable finite depth foliation in the complement of a link admits a presentation by a rectangular diagram compatible with the…
Penrose's work \cite{8} established a connection between the edge 3-colorings of cubic planar graphs and tensor algebras. We exploit this point of view in order to get algebraic representations of the category of cubic graphs with free…
Motivated by the theory of crystallizations, we consider an equivalence relation on the class of $3$-regular colored graphs and prove that up to this equivalence (a) there exists a unique contracted 3-regular colored graph if the number of…
We describe the images of multilinear polynomials of arbitrary degree evaluated on the $3\times 3$ upper triangular matrix algebra over an infinite field.
We present exact calculations of Potts model partition functions and the equivalent Tutte polynomials for polygon chain graphs with open and cyclic boundary conditions. Special cases of the results that yield flow and reliability…
Results of Koebe (1936), Schramm (1992), and Springborn (2005) yield realizations of $3$-polytopes with edges tangent to the unit sphere. Here we study the algebraic degrees of such realizations. This initiates the research on constrained…
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e. filiform Lie (super)algebras, into the theory of Lie algebras of order F$. Thus, the concept of filiform Lie algebras of order F is…
We introduce a majorization order on monomials. With the help of this order, we derive a necessary condition on the positive termination of a general successive difference substitution algorithm (KSDS) for an input form $f$.
We consider the problem of proving termination for triangular weakly non-linear loops (twn-loops) over some ring $\mathcal{S}$ like $\mathbb{Z}$, $\mathbb{Q}$, or $\mathbb{R}$. The guard of such a loop is an arbitrary quantifier-free…
A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite…
A given order type in the plane can be represented by a point set. However, it might be difficult to recognize the orientations of some point triples. Recently, Aichholzer \etal \cite{abh19} introduced exit graphs for visualizing order…
We provide a polynomial time 4/3 approximation algorithm for TSP on metrics arising from the metric completion of cubic 3-edge connected graphs.
This paper deals with graph classes characterization and recognition. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs. Unfortunately this strategy usually does not lead to an efficient…
In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We call such a decomposition the triple decomposition, and the…
The isomorphism problem for planar graphs is known to be efficiently solvable. For planar 3-connected graphs, the isomorphism problem can be solved by efficient parallel algorithms, it is in the class $AC^1$. In this paper we improve the…
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
In this short note we give an expression for some numbers $n$ such that the polynomial $x^{2p}-nx^p+1$ is reducible.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
Intersection graphs of geometric objects have been extensively studied, both due to their interesting structure and their numerous applications; prominent examples include interval graphs and permutation graphs. In this paper we study a…