Related papers: A class of reconstructible graphs
In this paper, we investigate a relation between finite graphs, simplicial flag complexes and right-angled Coxeter groups, and we provide a class of reconstructible finite graphs. We show that if $\Gamma$ is a finite graph which is the…
We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.
In this article, we use a unified approach to prove several classes of planar graphs are DP-$3$-colorable, which extend the corresponding results on $3$-choosability.
We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…
The graph reconstruction conjecture states that all graphs on at least three vertices are determined up to isomorphism by their deck. In this paper, a general framework for this problem is proposed to simply explain the reconstruction of…
In this paper, we classify reflexible regular Cayley maps for dihedral groups.
In this paper, we will consider the graph w*-probability theory.
We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. Some results about the visualization of…
Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.
We discuss a recursive formula for number of spanning trees in a graph. The paper is written primary for school students.
Many degree sequences can only be realised in graphs that contain a `ds-completable card', defined as a vertex-deleted subgraph in which the erstwhile neighbours of the deleted vertex can be identified from their degrees, if one knows the…
In this note we give a combinatorial characterization of all the unmixed bipartite graphs.
In this paper, we describe a reproduction of the Relational Graph Convolutional Network (RGCN). Using our reproduction, we explain the intuition behind the model. Our reproduction results empirically validate the correctness of our…
We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
We classify the connected-homogeneous digraphs with more than one end. We further show that if their underlying undirected graph is not connected-homogeneous, they are highly-arc-transitive.
This article discuss a class of tractable model in the form of polynomial type.
The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving…
A $k$-regular graph on $v$ vertices is a {\em divisible design graph} if there exist integers $\lambda_1,\lambda_2,m,n$ such that the vertex set can be partitioned into $m$ classes of size $n$ and any two different vertices from the same…