相关论文: Graph Operations on Clique-Width Bounded Graphs

The chromatic number of signed graphs is defined recently. The coloring and clique problem of interval graphs has been studied and polynomial time algorithms are established. Here we consider these problems for signed interval graphs and…

Finding a few solutions for a given problem that are diverse, as opposed to finding a single best solution to solve the problem, has recently become a notable topic in theoretical computer science. Recently, Baste, Fellows, Jaffke,…

We present a fixed-parameter tractable algorithm for first-order model checking on interpretations of graph classes with bounded local cliquewidth. Notably, this includes interpretations of planar graphs, and more generally, of classes of…

Extending several previous results we obtained nearly tight estimates on the maximum size of a clique-minor in various classes of expanding graphs. These results can be used to show that graphs without short cycles and other H-free graphs…

Motivated by recently discovered privacy attacks on social networks, we study the problem of anonymizing the underlying graph of interactions in a social network. We call a graph (k,l)-anonymous if for every node in the graph there exist at…

Merge-width is a recently introduced family of graph parameters that unifies treewidth, clique-width, twin-width, and generalised colouring numbers. We prove the equivalence of several alternative definitions of merge-width, thus…

In this paper we give upper bounds on the number of minimal separators and potential maximal cliques of graphs w.r.t. two graph parameters, namely vertex cover ($\operatorname{vc}$) and modular width ($\operatorname{mw}$). We prove that for…

In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…

In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that…

Given a clique-width $k$-expression of a graph $G$, we provide $2^{O(k)}\cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex…

Ray intersection graphs are intersection graphs of rays, or halflines, in the plane. We show that any planar graph has an even subdivision whose complement is a ray intersection graph. The construction can be done in polynomial time and…

A graph is inductive $k$-independent if there exists and ordering of its vertices $v_{1},...,v_{n}$ such that $\alpha(G[N(v_{i})\cap V_{i}])\leq k $ where $N(v_{i})$ is the neighborhood of $v_{i}$, $V_{i}=\{v_{i},...,v_{n}\}$ and $\alpha$…

A graph $G$ of order $nv$ where $n\geq 2$ and $v\geq 2$ is said to be weakly $(n,v)$-clique-partitioned if its vertex set can be decomposed in a unique way into $n$ vertex-disjoint $v$-cliques. It is strongly $(n,v)$-clique-partitioned if…

A cocomparability graph is a graph whose complement admits a transitive orientation. An interval graph is the intersection graph of a family of intervals on the real line. In this paper we investigate the relationships between interval and…

We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets (denoted IDENTIFYING CODE, (OPEN) LOCATING-DOMINATING SET and METRIC DIMENSION) of an interval or a permutation graph. In…

Motivated by an approach to visualization of high dimensional statistical data given in Hurley and Oldford (2011), this work examines the clique structure of $J_n(m, m-1)$ Johnson graphs. Cliques and maximal cliques are characterized and…

We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters,…

A \emph{clique} is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with $n$ vertices and $m$ edges; (2) graphs with $n$ vertices, $m$ edges,…

A map graph is a graph admitting a representation in which vertices are nations on a spherical map and edges are shared curve segments or points between nations. We present an explicit fixed-parameter tractable algorithm for recognizing map…

We show that every graph with twin-width $t$ has chromatic number $O(\omega ^{k_t})$ for some integer $k_t$, where $\omega$ denotes the clique number. This extends a quasi-polynomial bound from Pilipczuk and Soko{\l}owski and generalizes a…