Related papers: On Finding Lekkerkerker-Boland Subgraphs

This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…

We study the problem of finding a maximum cardinality minimal separator of a graph. This problem is known to be NP-hard even for bipartite graphs. In this paper, we strengthen this hardness by showing that for planar bipartite graphs, the…

In this paper we show that every graph of pathwidth less than $k$ that has a path of order $n$ also has an induced path of order at least $\frac{1}{3} n^{1/k}$. This is an exponential improvement and a generalization of the polylogarithmic…

In his pioneering paper on matroids in 1935, Whitney obtained a characterization for binary matroids and left a comment at end of the paper that the problem of characterizing graphic matroids is the same as that of characterizing matroids…

The class of intersection bigraphs of unit intervals of the real line whose ends may be open or closed is called a class of mixed unit interval bigraphs. This class of bigraphs is a strict superclass of the class of unit interval bigraphs.…

The 0-1 matrix A contains a 0-1 matrix M if some submatrix of A can be transformed into M by changing some ones to zeroes. If A does not contain M, then A avoids M. Let ex(n,M) be the maximum number of ones in an n x n 0-1 matrix that…

In a labeling scheme the vertices of a given graph from a particular class are assigned short labels such that adjacency can be algorithmically determined from these labels. A representation of a graph from that class is given by the set of…

The problem of enumerating connected subgraphs of a given size in a graph has been extensively studied in recent years. In this paper, we propose an algorithm with a delay of $O(k\Delta)$ for enumerating all connected induced subgraphs of…

Although there are very algorithms for embedding graphs on unbounded grids, only few results on embedding or drawing graphs on restricted grids has been published. In this work, we consider the problem of embedding paths and cycles on grid…

Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology \cite{Civan}, and the framework through which it was studied, we introduce the linear coloring on graphs. We…

An odd hole in a graph is a induced cycle with odd length greater than 3. In an earlier paper (with Sophie Spirkl), solving a longstanding open problem, we gave a polynomial-time algorithm to test if a graph has an odd hole. We subsequently…

Enumerating minimal transversals in a hypergraph is a notoriously hard problem. It can be reduced to enumerating minimal dominating sets in a graph, in fact even to enumerating minimal dominating sets in an incomparability graph. We provide…

We characterise the structure of those graphs of a given order which maximise the number of connected induced subgraphs for seven different graph classes, each with other prescribed parameters like minimum degree, independence number,…

It is known that the class of all graphs not containing a graph $H$ as an induced subgraph is cop-bounded if and only if $H$ is a forest whose every component is a path. In this study, we characterize all sets $\mathscr{H}$ of graphs with…

We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a…

Let $G=(V,E)$ be a simple graph without isolated vertices. A set $S\subseteq V$ is a paired-dominating set if every vertex in $V-S$ has at least one neighbor in $S$ and the subgraph induced by $S$ contains a perfect matching. In this paper,…

In this paper, we propose a polynomial-time algorithm to test whether a given graph contains a subdivision of $K_4$ as an induced subgraph.

This paper presents a new graph isomorphism invariant, called $\mathfrak{w}$-labeling, that can be used to design a polynomial-time algorithm for solving the graph isomorphism problem for various graph classes. For example, all…

A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following…

We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…