Related papers: Integrable deformations of systems on graphs with …
We present infinitely many nonlocal conservation laws, a pair of compatible local Hamiltonian structures and a recursion operator for the equations describing surfaces in three-dimensional space that admit nontrivial deformations which…
There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we may establish a new method, the intrinsic regularization…
It is shown that each subgroup of odd index in an alternating group of degree at least 10 has all insoluble composition factors to be alternating. A classification is then given of 2-arc-transitive graphs of odd order admitting an…
In a coupled network cells can interact in several ways. There is a vast literature from the last twenty years that investigates this interacting dynamics under a graph theory formalism, namely as a graph endowed with an input-equivalence…
The survey provides classification results for integrable one-field evolution equations of orders 2, 3 and 5 with the constant separant. The classification is based on necessary integrability conditions following from the existence of the…
A graph $G$ has a $C_k$-decomposition if its edge set can be partitioned into cycles of length $k$. We show that if $\delta(G)\geq 2|G|/3-1$, then $G$ has a $C_4$-decomposition, and if $\delta(G)\geq |G|/2$, then $G$ has a…
An analysis of necessary conditions for the existence of controlled dynamics with an attractor of a specified topological type is given. It uses the Hopf classification by degree for Gauss maps of manifolds to spheres of the same dimension,…
A graph $G=(V,E)$ is representable if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)\in E$ for each $x\neq y$. If $W$ is $k$-uniform (each letter of $W$ occurs exactly $k$…
In this paper we consider the complex uniformly resolvable decompositions of the complete graph $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph from a given set $\mathcal H$. We…
We show that for any $d\ge 2$ and $\Delta>0$ there exists $\eta>0$ such that the following holds: Let $G$ be an $n$-vertex graph with at least $\Omega(n^2)$ edges and let $H$ be an $n$-vertex $d$-degenerate graph with maximum degree at most…
A graph $G$ is $k$-degenerate if it can be transformed into an empty graph by subsequent removals of vertices of degree $k$ or less. We prove that every connected planar graph with average degree $d \ge 2$ has a 4-degenerate induced…
We prove two mixed versions of the Discrete Nodal Theorem of Davies et. al. [3] for bounded degree graphs, and for three-connected graphs of fixed genus $g$. Using this we can show that for a three-connected graph satisfying a certain…
An $[a,b]$-factor of a graph $G$ is a spanning subgraph $H$ such that $a\leq d_{H}(v)\leq b$ for each $v\in V(G)$. In this paper, we provide spectral conditions for the existence of an odd $[1,b]$-factor in a connected graph with minimum…
Let $A = \Bbbk Q / I$ be the path algebra of any finite quiver $Q$ modulo any two-sided ideal $I$ of relations and let $R$ be any reduction system satisfying the diamond condition for $I$. We introduce an intrinsic notion of deformation of…
We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number…
Let $\mu(G)$ denote the spectral radius of a graph $G$. We partly confirm a conjecture due to Nikiforov, which is a spectral radius analogue of the well-known Erd\H{o}s-S\'os Conjecture that any tree of order $t$ is contained in a graph of…
Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the…
Relying on the redefined vacuum state approach, and based on one-particle three-loop Feynman diagrams, partial third-order interelectronic corrections to the valence electron energy shift are investigated in Li-like ions. The idea is to…
We show that for all simple graphs G other than the cycles C_3,C_4,C_5, and the claw K_1,3 there exists a K > 0 such that whenever k > K the k-th iterate of the line graph can be distinguished by at most two colors. Additionally we…
In this paper we consider the uniformly resolvable decompositions of the complete graph $2K_v$ into subgraphs where each resolution class contains only blocks isomorphic to the same graph. We completely determine the spectrum for the cases…