Related papers: Graph classes and forbidden patterns on three vert…
A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…
A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition…
We describe and implement two local reduction rules that can be used to recognize Halin graphs in linear time, avoiding the complicated planarity testing step of previous linear time Halin graph recognition algorithms. The same two rules…
Let k be a natural number. We introduce k-threshold graphs. We show that there exists an O(n^3) algorithm for the recognition of k-threshold graphs for each natural number k. k-Threshold graphs are characterized by a finite collection of…
Several graph properties are characterized as the class of graphs that admit an orientation avoiding finitely many oriented structures. For instance, if $F_k$ is the set of homomorphic images of the directed path on $k+1$ vertices, then a…
Graph neural networks (GNNs) have achieved great success in many scenarios with graph-structured data. However, in many real applications, there are three issues when applying GNNs: graphs are unknown, nodes have noisy features, and graphs…
The implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined…
Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…
A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was…
Risk classification plays an important role in many regulations and standards. However, a general method that provides an optimal classification has not been proposed yet. Also, the criteria of optimality are not defined in these…
Path graphs are intersection graphs of paths in a tree.~In this paper we give a "6\ good characterization" of path graphs, namely, we prove that path graph membership is in $NP\cap CoNP$ without resorting to existing polynomial time…
A graph is a path graph if it is the intersection graph of a family of subpaths of a tree. In 1970, Renz asked for a characterizaton of path graphs by forbidden induced subgraphs. Here we answer this question by listing all graphs that are…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
We introduce the class of circular-arc H-graphs, which generalizes circular-arc graphs, particularly circular-arc bigraphs. We investigate two types of ordering-based characterizations of circular-arc r-graphs. Finally, we provide forbidden…
A graph is concave-round if its vertices can be circularly enumerated so that the closed neighbourhood of each vertex is an interval in the enumeration. In this work, we give a minimal forbidden induced subgraph characterization for the…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged.…
In a paired threshold graph, each vertex has a weight, and two vertices are adjacent if their weight sum is large enough and their weight difference is small enough. It generalizes threshold graphs and unit interval graphs, both very well…
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…
Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…