Related papers: Non-Hamiltonian 2-regular Digraphs -- Residues

In the present paper correspondence between non-Noether symmetries and bi-Hamiltonian structures is disscussed. We show that in regular Hamiltonian systems presence of the global bi-Hamiltonian structure is caused by symmetry of the space…

There is empirical evidence supporting the claim that almost all cubic non-Hamiltonian graphs are bridge graphs. In this paper, we pose a related conjecture and prove that the original claim holds for non-3-connected graphs if the…

A graph $\textit{G}$ is a tuple $(\textit{V}, \textit{E})$, where $\textit{V}$ is the vertex set, $\textit{E}$ is the edge set. A reduced graph is a graph of deleting non-Hamiltonian edges and smoothing out the redundant vertices of degree…

We consider Hamilton cycles in the random digraph $D_{n,m}$ where the orientation of edges follows a pattern other than the trivial orientation in which the edges are oriented in the same direction as we traverse the cycle. We show that if…

We consider a 2-complex in a particular form, called the Quinn model of a 2-complex. It can be sliced in graphs, where a change from one graph to another can be organized by a sequence of local transitions, which are described in a list of…

For a connected graph, a path containing all vertices is known as \emph{Hamiltonian path}. For general graphs, there is no known necessary and sufficient condition for the existence of Hamiltonian paths and the complexity of finding a…

We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes…

We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV…

We study biplane graphs drawn on a finite planar point set $S$ in general position. This is the family of geometric graphs whose vertex set is $S$ and can be decomposed into two plane graphs. We show that two maximal biplane graphs---in the…

In this paper, we study the Hamiltonicity of graphs with large minimum degree. Firstly, we present some conditions for a simple graph to be Hamilton-connected and traceable from every vertex in terms of the spectral radius of the graph or…

We introduce a general construction on 2-monads. We develop background on maps of 2-monads, their left semi-algebras, and colimits in 2-category. Then, we introduce the construction of a colimit induced by a map of 2-monads, show that we…

Let $\mathbb{P}^s$ be the $s$-dimensional complex projective space, and let $X, Y$ be two non-empty open subsets of $\mathbb{P}^s$ in the Zariski topology. A hypersurface $H$ in $\mathbb{P}^s\times\mathbb{P}^s$ induces a bipartite graph $G$…

We study noncommutative differential structures on the group of permutations $S_N$, defined by conjugacy classes. The 2-cycles class defines an exterior algebra $\Lambda_N$ which is a super analogue of the Fomin-Kirillov algebra $\CE_N$ for…

In this paper, we describe all invariant distributions of non-degenerate bi-Hamiltonian structures and investigate their integrability in the neighbourhood of a generic point.

We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, $K_{h+1}$-minor-free,…

The Hermitian adjacency matrices of digraphs based on the sixth root of unity were introduced in [B. Mohar, A new kind of Hermitian matrices for digraphs, Linear Alg. Appl. (2020)]. They appear to be the most natural choice for the spectral…

Bifurcations of the $A_{n}$ type in Arnold's classification, in non-autonomous $p$-periodic difference equations generated by parameter depending families with $p$ maps, are studied. It is proved that the conditions of degeneracy,…

A simple undirected graph is said to be {\em semisymmetric} if it is regular and edge-transitive but not vertex-transitive. Every semisymmetric graph is a bipartite graph with two parts of equal size. It was proved in [{\em J. Combin.…

In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries and conserved quantities in the language of commutant algebras. In particular, we start with families of…

The well-known characterization of two-ended groups says that every two-ended group can be split over finite subgroups which means it is isomorphic to either by a free product with amalgamation $A\ast_C B$ or an HNN-extension $\ast_{\phi}…