Related papers: Maximum Independent Set when excluding an induced …

We confirm a conjecture of Gartland and Lokshtanov [arXiv:2007.08761]: if for a hereditary graph class $\mathcal{G}$ there exists a constant $k$ such that no member of $\mathcal{G}$ contains a $k$-creature as an induced subgraph or a…

Maximal independent set (MIS), maximal matching (MM), and $(\Delta+1)$-coloring in graphs of maximum degree $\Delta$ are among the most prominent algorithmic graph theory problems. They are all solvable by a simple linear-time greedy…

For an arbitrary undirected simple graph G with m edges, we give an algorithm with running time O(m^4 |L|^2) to generate the set L of all minimal edge dominating sets of G. For bipartite graphs we obtain a better result; we show that their…

The Isolation Lemma of Mulmuley, Vazirani and Vazirani [Combinatorica'87] provides a self-reduction scheme that allows one to assume that a given instance of a problem has a unique solution, provided a solution exists at all. Since its…

We investigate the distributed complexity of maximal matching and maximal independent set (MIS) in hypergraphs in the LOCAL model. A maximal matching of a hypergraph $H=(V_H,E_H)$ is a maximal disjoint set $M\subseteq E_H$ of hyperedges and…

Minimal separators in graphs are an important concept in algorithmic graph theory. In particular, many problems that are NP-hard for general graphs are known to become polynomial-time solvable for classes of graphs with a polynomially…

In this paper, we develop efficient exact and approximate algorithms for computing a maximum independent set in random graphs. In a random graph $G$, each pair of vertices are joined by an edge with a probability $p$, where $p$ is a…

In the Independent Set Reconfiguration problem under the Token Addition/Removal rule, given a graph $G$ and two independent sets $I$ and $J$ of $G$, we want to transform $I$ into $J$ by adding and removing vertices, such that all the sets…

\emph{Strictly Chordality-$k$ graphs ($SC_k$)} are graphs which are either cycle-free or every induced cycle is of length exactly $k, k \geq 3$. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal…

We prove that a number of computational problems that ask for the largest sparse induced subgraph satisfying some property definable in CMSO2 logic, most notably Feedback Vertex Set, are polynomial-time solvable in the class of $P_6$-free…

The classic theorem of Gallai and Milgram (1960) generalizes several fundamental results in Graph Theory, such as Dilworth's theorem on posets and K\H{o}nig's theorem on matchings in bipartite graphs. The theorem asserts that for every…

For any finite set $\mathcal{H} = \{H_1,\ldots,H_p\}$ of graphs, a graph is $\mathcal{H}$-subgraph-free if it does not contain any of $H_1,\ldots,H_p$ as a subgraph. In recent work, meta-classifications have been studied: these show that if…

We give the first polynomial-time algorithms on graphs of bounded maximum induced matching width (mim-width) for problems that are not locally checkable. In particular, we give $n^{\mathcal{O}(w)}$-time algorithms on graphs of mim-width at…

The complexity of {\sc Colouring} is fully understood for $H$-free graphs, but there are still major complexity gaps if two induced subgraphs $H_1$ and $H_2$ are forbidden. Let $H_1$ be the $s$-vertex cycle $C_s$ and $H_2$ be the $t$-vertex…

In the well known planted clique problem, a clique (or alternatively, an independent set) of size $k$ is planted at random in an Erdos-Renyi random $G(n, p)$ graph, and the goal is to design an algorithm that finds the maximum clique (or…

Maximum weight independent set (MWIS) admits a $\frac1k$-approximation in inductively $k$-independent graphs and a $\frac{1}{2k}$-approximation in $k$-perfectly orientable graphs. These are a a parameterized class of graphs that generalize…

The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…

The independent set on a graph $G=(V,E)$ is a subset of $V$ such that no two vertices in the subset have an edge between them. The MIS problem on $G$ seeks to identify an independent set with maximum cardinality, i.e. maximum independent…

We study unit ball graphs (and, more generally, so-called noisy uniform ball graphs) in $d$-dimensional hyperbolic space, which we denote by $\mathbb{H}^d$. Using a new separator theorem, we show that unit ball graphs in $\mathbb{H}^d$…

We prove new complexity results for Feedback Vertex Set and Even Cycle Transversal on $H$-free graphs, that is, graphs that do not contain some fixed graph $H$ as an induced subgraph. In particular, we prove that for every $s\geq 1$, both…