Related papers: Naji's characterization of circle graphs

Let $G$ be a simple graph on $n$ vertices and $\mathcal{I}_G$ denotes parity binomial edge ideal of $G$ in the polynomial ring $S = \mathbb{K}[x_1,\ldots, x_n, y_1, \ldots, y_n].$ We obtain a lower bound for the regularity of parity…

In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…

Let $J_G$ be the binomial edge ideal of a graph $G$. We characterize all graphs whose binomial edge ideals, as well as their initial ideals, have regularity $3$. Consequently we characterize all graphs $G$ such that $J_G$ is extremal…

In this paper we present a characterisation, by an infinite family of minimal forbidden induced subgraphs, of proper circular arc graphs which are intersection graphs of paths on a grid, where each path has at most one bend (turn).

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

These notes are a self-contained short proof of the stability of persistence diagrams.

In the present paper we show that the spectrum of an arbitrary starlike graph can be completely determined via separating functions $\rho_t$ (see \cite{NazRoi,RedRoi,Red3}). This fact helps to get in an easy way several results for the…

We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.

In this short note we use results from the theory of crystallizations to prove that color in group field theories garantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. The origin…

We determine the symmetrized topological complexity of the circle, using primarily just general topology.

Let $\Gamma(n,k)$ be the set of $2$-connected $n$-vertex graphs containing an edge that is not on any cycle of length at least $k+1.$ Let $g_s(n,k)$ denote the maximum number of $s$-cliques in a graph in $\Gamma(n,k).$ Recently, Ji and Ye…

We produce a new, shorter construction of a minor-universal planar graph.

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

A class of graphs is $\chi$-bounded if there exists a function $f:\mathbb N\rightarrow \mathbb N$ such that for every graph $G$ in the class and an induced subgraph $H$ of $G$, if $H$ has no clique of size $q+1$, then the chromatic number…

We give a simple graph-theoretic proof of a classical result due to C. St. J. A. Nash-Williams on covering graphs by forests. Moreover we derive a slight generalisation of this statement where some edges are preassigned to distinct forests.

The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

In previous work we determined automorphism groups of cyclic algebraic curves defined over fields of any odd characteristic. In this paper we determine parametric equations of families of curves for each automorphism group for such curves.

We give a sharp spectral condition for the existence of odd cycles in a graph of given order. We also prove a related stability result.

We characterise gaps in the full homomorphism order of graphs.