Related papers: Strongly chordal digraphs and $\Gamma$-free matric…
A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their…
Chordal graphs are important in the structural and algorithmic graph theory. A digraph analogue of chordal graphs was introduced by Haskin and Rose in 1973 but has not been a subject of active studies until recently when a characterization…
Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs,…
Let $G$ be a finite group. The \textit{commuting/nilpotent/solvable conjugacy class graph} ($\Gamma_{CCC}(G)$, $\Gamma_{NCC}(G)$, or $\Gamma_{SCC}(G)$) is a simple graph whose vertex set consists of all non-central conjugacy classes of $G$.…
The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater…
Jerrum, Sinclair and Vigoda (2004) showed that the permanent of any square matrix can be estimated in polynomial time. This computation can be viewed as approximating the partition function of edge-weighted matchings in a bipartite graph.…
A bipartite graph is chordal bipartite if every cycle of length at least 6 has a chord in it. In this paper, we investigate the structure of $P_5$-free chordal bipartite graphs and show that these graphs have a Nested Neighborhood Ordering,…
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…
A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
The concept of graph powers has been extensively studied in graph theory. Analogous to graph powers, Chandran et al. [3] introduced the notion of bipartite powers for bipartite graphs. In this paper, we show that the class of interval…
In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given in \cite{VT}, so that a triangulated hypergraph, according to our definition, is a natural…
We focus on strongly connected, strong for short, digraphs since in this setting distance is defined for every pair of vertices. Distance ideals generalize the spectrum and Smith normal form of several distance matrices associated with…
In this paper, we show the existence of a polynomial time graph isomorphism algorithm for all graphs excluding graphs that are locally trianglefree. This particular class of graphs allows to divide the graph into neighbourhood sub-graph…
Chordal graphs and chordal bigraphs enjoy beautiful characterizations, in terms of forbidden subgraphs, vertex/edge orderings, vertex/edge separating sets, and tree-like representations. In this paper, we introduce chordal signed graphs and…
We prove that the class of chordal graphs is easily testable in the following sense. There exists a constant $c>0$ such that, if adding/removing at most $\epsilon n^2$ edges to a graph $G$ with $n$ vertices does not make it chordal, then a…
A graph is called chordal if it forbids induced cycles of length 4 or more. In this paper, we attempt to identify the non-nilpotent groups whose power graph is a chordal graph (this question was raised by Cameron in [4]). In this direction,…
We consider the problem of devising algorithms to count exactly the number of independent sets of a graph G . We show that there is a polynomial time algorithm for this problem when G is restricted to the class of strongly orderable graphs,…
In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. An important property common for both of them is well-quasi-orderability, implying, in a…
The sun is the graph obtained from a cycle of length even and at least six by adding edges to make the even-indexed vertices pairwise adjacent. Suns play an important role in the study of strongly chordal graphs. A graph is chordal if it…