Related papers: Recognizing and generating unswitchable graphs
We show that in contrast to the Rado graph, the Henson graphs are not computably indivisible.
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 introduce a characterization for split graphs by using edge contraction. Then, we use it to prove that any ($2K_{2}$, claw)-free graph with $\alpha(G) \geq 3$ is a split graph. Also, we apply it to characterize any pseudo-split graph.…
We propose a novel and trainable graph unpooling layer for effective graph generation. Given a graph with features, the unpooling layer enlarges this graph and learns its desired new structure and features. Since this unpooling layer is…
A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide, to the best of our knowledge, the first characterization of…
A split graph is a graph whose vertices can be partitioned into a clique and a stable set. We investigate the combinatorial species of split graphs, providing species-theoretic generalizations of enumerative results due to B\'ina and…
A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$…
This paper has dual aims. First is to develop practical universal coding methods for unlabeled graphs. Second is to use these for graph anomaly detection. The paper develops two coding methods for unlabeled graphs: one based on the degree…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A connected graph $G$ is said to be $t$-admissible if admits a spanning tree in which the distance between any two adjacent vertices of $G$…
We present a construction that gives an infinite series of divisible design graphs which are Cayley graphs.
A graph $G=(V,E)$ is a {\it unipolar graph} if there exits a partition $V=V_1 \cup V_2$ such that, $V_1$ is a clique and $V_2$ induces the disjoint union of cliques. The complement-closed class of {\it generalized split graphs} are those…
In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class $\mathcal{G}$, we are concerned with the maximum subclass and the minimum superclass of $\mathcal{G}$ that…
Unigraphs are graphs identifiable up to isomorphism from their degree sequences. Given a class $\mathcal{A}$ of graphs, we define the class of $\mathcal{A}$-unigraphs to be graphs identifiable from degree sequence and membership in…
Graph generation is one of the most challenging tasks in recent years, and its core is to learn the ground truth distribution hiding in the training data. However, training data may not be available due to security concerns or unaffordable…
In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These graphs are characterized in terms of the non-ancestor graphs of rooted trees.
The most elusive problem around the class of circular-arc graphs is identifying all minimal graphs that are not in this class. The main obstacle is the lack of a systematic way of enumerating these minimal graphs. McConnell [FOCS 2001]…
A classification is given of all the countable homogeneous ordered bipartite graphs.
Graphs are ubiquitous real-world data structures, and generative models that approximate distributions over graphs and derive new samples from them have significant importance. Among the known challenges in graph generation tasks,…
Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications -- addition and removal of vertices and/or edges -- in the graph.…