Related papers: The computational strength of matchings in countab…
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…
Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul\'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges…
Let $G$ be a connected simple graph on $n$ vertices and $m$ edges. Denote $N_{i}^{(j)}(G)$ the number of spanning subgraphs of $G$ having precisely $i$ edges and not more than $j$ connected components. The graph $G$ is \emph{strong} if…
We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdos and Renyi about perfect matchings in random bipartite graphs.…
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…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
A matchstick graph is a crossing-free unit-distance graph in the plane. Harborth (1981) proposed the problem of determining whether there exists a matchstick graph in which every vertex has degree exactly $5$. In 1982, Blokhuis gave a proof…
We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space $\mathbb{X}$ equipped with a continuous function $f: \mathbb{X} \rightarrow \mathbb{R}$. We first give a categorification of the…
Knowledge graph embeddings (KGEs) were originally developed to infer true but missing facts in incomplete knowledge repositories. In this paper, we link knowledge graph completion and counterfactual reasoning via our new task CFKGR. We…
Let $F_G(P)$ be a functional defined on the set of all the probability distributions on the vertex set of a graph $G$. We say that $G$ is \emph{symmetric with respect to $F_G(P)$} if the uniform distribution on $V(G)$ maximizes $F_G(P)$.…
This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…
We present an algebraic characterization of perfect graphs, i.e., graphs for which the clique number and the chromatic number coincide for every induced subgraph. We show that a graph is perfect if and only if certain nonnegative…
Let $f$ be a postcritically finite rational map. We prove that, as $n$ large enough, there exists an $f^n$-invariant (finite connected) graph on $\widehat{\mathbb{C}}$ such that it contains the postcritical set of $f$.
Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of mathematics, including number theory, finite algebra,…
An induced matching in a graph is a set of edges whose endpoints induce a $1$-regular subgraph. Gupta et al. (2012,\cite{Gupta}) showed that every $n$-vertex graph has at most $10^{\frac{n}{5}}\approx 1.5849^n$ maximal induced matchings,…
A graph $G$ is called matching covered if all of its edges are contained in some perfect matching of $G$. Furthermore, a cycle $C \subseteq G$ is called conformal if $G - V(C)$ has a perfect matching and $G$ itself is called cycle-conformal…
Given a graph $G$, the matching number of $G$, written $\alpha'(G)$, is the maximum size of a matching in $G$, and the fractional matching number of $G$, written $\alpha'_f(G)$, is the maximum size of a fractional matching of $G$. In this…
We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erd\H{o}s-R\'enyi graphs $\mathcal{G}(n,q)$ whose edges are…