Related papers: Naji's characterization of circle graphs

We consider Stanley--Reisner rings $k[x_1,...,x_n]/I(\mc{H})$ where $I(\mc{H})$ is the edge ideal associated to some particular classes of hypergraphs. For instance, we consider hypergraphs that are natural generalizations of graphs that…

We compute numerically the homology of several graph complexes in low loop orders, extending previous results.

We prove that computing a single pair of vertices that are mapped onto each other by an isomorphism $\phi$ between two isomorphic graphs is as hard as computing $\phi$ itself. This result optimally improves upon a result of G\'{a}l et al.…

In this paper, we give a characterization of distance matrices of distance-regular graphs to be invertible.

We give a simplified proof of analyticity of pluripolar multifunctions

We give a characterization of isomorphisms between Schreier graphs in terms of the groups, subgroups and generating systems. This characterization may be thought as a graph analog of Mostow's rigidity theorem for hyperbolic manifolds. This…

It is shown that shift graphs can be realized as disjointness graphs of 1-intersecting curves in the plane. This implies that the latter class of graphs is not $\chi$-bounded.

We exhibit infinitely many examples of edge-regular graphs that have regular cliques and that are not strongly regular. This answers a question of Neumaier from 1981.

We prove a few simple cases of a random graph statement that would imply the "second" Kahn--Kalai Conjecture. Even these cases turn out to be reasonably challenging, and it is hoped that the ideas introduced here may lead to further…

We present explicit descriptions of the decompositions of vertices of a hypercube graph with respect to its distinguished symmetric cycle.

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper we prove that if $G$ is a unicyclic graph then for all $s \geq 1$ the regularity of $I(G)^s$ is exactly $2s+\text{reg}(I(G))-2$. We also…

In this paper, we will consider the graph w*-probability theory.

In this short note, we prove the uniqueness of exterior differentiation on locally finite graphs.

We give upper bounds on the order of the automorphism group of a simple graph

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

On the simultaneous edge coloring of graphs

By defining grids as graphs, geometric graphs can be represented in a very concise way.

We improve the estimates of the subgraph probabilities in a random regular graph. Using the improved results, we further improve the limiting distribution of the number of triangles in random regular graphs.

In this paper, we discuss $J$-colouring of the family of Jahangir graphs. Note that the family of Jahangir graphs is a wide-ranging family of graphs which by a generalised definition includes wheel graphs. We characterise the subset of…

In this paper, we present a short proof of Halin's grid theorem.