Related papers: Naji's characterization of circle graphs

Let $G$ be a graph on $n$ vertices and $C'=v_0v_1\cdots v_{p-1}v_0$ a vertex sequence of $G$ with $p\geq 3$ ($v_i\neq v_j$ for all $i,j=0,1,\ldots,p-1$, $i\neq j$). If for any successive vertices $v_i$, $v_{i+1}$ on $C'$, either…

The circumference denoted by $c(G)$ of a graph $G$ is the length of its longest cycle. Let $\delta(G)$ and $\omega(G)$ denote the minimum degree and the clique number of a graph $G$, respectively. In [\emph{Electron. J. Combin.} 31(4)(2024)…

In this note, finite type epimorphisms of rings are characterized.

We characterize $k$--colorability of a simplicial graph via the intrinsic algebraic structure of the associated right-angled Artin group. As a consequence, we show that a certain problem about the existence of homomorphisms from…

The main theorem of "S. J. Kov\'acs: The cone of curves of a K3 surface, Math. Ann. 300 (1994), no. 4, 681-691" is proved in arbitrary characteristic. The proof is essentially the same as in the original paper where it was stated only over…

The goal of this paper is to describe a sufficient condition on cycles in graphs for which the edge ideal is splittable. We give an explicit splitting function for such ideals.

Cayley graphs are graphs on algebraic structures, typically groups or group-like structures. In this paper, we have obtained a few results on Cayley graphs on Cyclic groups, powers of cycles, Cayley graphs on some non-abelian groups, and…

We introduce four new elementary short proofs of the famous K\"onig's theorem which characterizes bipartite graphs by absence of odd cycles.

In this note, we provide a proof of a technical result of Erd\H{o}s and Hajnal about the existence of disjoint type graphs with no odd cycles. We also prove that this result is sharp in a certain sense.

Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.

We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.

For integers $k \geq 2$ and $n \geq k+1$, we prove the following: If $n\cdot k$ is even, there is a connected $k$-regular graph on $n$ vertices. If $n\cdot k$ is odd, there is a connected nearly $k$-regular graph on $n$ vertices.

We provide an annotated bibliography for the study of Hamilton cycles in random graphs and hypergraphs.

We prove a lower bound on the length of the longest $j$-tight cycle in a $k$-uniform binomial random hypergraph for any $2 \le j \le k-1$. We first prove the existence of a $j$-tight path of the required length. The standard "sprinkling"…

In this note, we prove a certain hypergraph generalization of the Balog-Szemeredi-Gowers Theorem. Our result shares some features in common with a similar such generalizsation due to Sudakov, Szemeredi and Vu, though the conclusion of our…

We give a simple proof of MacLane's algebraic planarity criterion for graphs. This proof does not use any other known planarity criteria. Keywords: graph, planarity, cycle space, a simple basis of a graph.

In this note we extend a theorem from [13] about uniform circle random coverings

We state and prove a correct version of a theorem presented in an earlier paper.

We define the notion of a twisted topological graph algebra associated to a topological graph and a $1$-cocycle on its edge set. We prove a stronger version of a Vasselli's result. We expand Katsura's results to study twisted topological…

We characterise when a set of simple closed curves in an orientable surface forms a bouquet, in terms of relations between the corresponding Dehn twists.