Related papers: A Polynomial Kernel for Line Graph Deletion
Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…
In the presented paper we study the Length-Bounded Cut problem for special graph classes as well as from a parameterized-complexity viewpoint. Here, we are given a graph $G$, two vertices $s$ and $t$, and positive integers $\beta$ and…
We show that the k-Dominating Set problem is fixed parameter tractable (FPT) and has a polynomial kernel for any class of graphs that exclude K_{i,j} as a subgraph, for any fixed i, j >= 1. This strictly includes every class of graphs for…
The F-Minor-Free Deletion problem asks, for a fixed set F and an input consisting of a graph G and integer k, whether k vertices can be removed from G such that the resulting graph does not contain any member of F as a minor. This paper…
Given a family of graphs $\mathcal{H}$, a graph $G$ is $\mathcal{H}$-free if any subset of $V(G)$ does not induce a subgraph of $G$ that is isomorphic to any graph in $\mathcal{H}$. We present sufficient and necessary conditions for a graph…
We consider undirected simple finite graphs. The sets of vertices and edges of a graph $G$ are denoted by $V(G)$ and $E(G)$, respectively. For a graph $G$, we denote by $\delta(G)$ and $\eta(G)$ the least degree of a vertex of $G$ and the…
The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. By appropriately introducing a weight to each edge of a graph, we determine, among other thing, the skewness of the generalized Petersen…
The MULTICUT IN TREES problem consists in deciding, given a tree, a set of requests (i.e. paths in the tree) and an integer k, whether there exists a set of k edges cutting all the requests. This problem was shown to be FPT by Guo and…
Massive network exploration is an important research direction with many applications. In such a setting, the network is, usually, modeled as a graph $G$, whereas any structural information of interest is extracted by inspecting the way…
The Chordal Vertex Deletion (ChVD) problem asks to delete a minimum number of vertices from an input graph to obtain a chordal graph. In this paper we develop a polynomial kernel for ChVD under the parameterization by the solution size, as…
An intersection graph of curves in the plane is called a string graph. Matousek almost completely settled a conjecture of the authors by showing that every string graph of m edges admits a vertex separator of size O(\sqrt{m}\log m). In the…
We consider a graph polynomial \xi(G;x,y,z) introduced by Averbouch, Godlin, and Makowsky (2007). This graph polynomial simultaneously generalizes the Tutte polynomial as well as a bivariate chromatic polynomial defined by Dohmen, Poenitz…
Let $G(V, E)$ be a simple connected graph, with $|E| = \epsilon.$ In this paper, we define an edge-set graph $\mathcal G_G$ constructed from the graph $G$ such that any vertex $v_{s,i}$ of $\mathcal G_G$ corresponds to the $i$-th…
The classical Menger's theorem states that in any undirected (or directed) graph $G$, given a pair of vertices $s$ and $t$, the maximum number of vertex (edge) disjoint paths is equal to the minimum number of vertices (edges) needed to…
In the $k$-Leaf Out-Branching and $k$-Internal Out-Branching problems we are given a directed graph $D$ with a designated root $r$ and a nonnegative integer $k$. The question is to determine the existence of an outbranching rooted at $r$…
The "edge polytope" of a finite graph G is the convex hull of the columns of its vertex-edge incidence matrix. We study extremal problems for this class of polytopes. For k =2, 3, 5 we determine the maximum number of vertices of…
A graph $G$ is $k$-critical if $G$ is not $(k-1)$-colorable, but every proper subgraph of $G$ is $(k-1)$-colorable. A graph $G$ is $k$-choosable if $G$ has an $L$-coloring from every list assignment $L$ with $|L(v)|=k$ for all $v$, and a…
In this paper, we address problems related to parameters concerning edge mappings of graphs. The quantity $h(n,G)$ is defined to be the maximum number of edges in an $n$-vertex graph $H$ such that there exists a mapping $f: E(H)\rightarrow…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
For an edge-colored graph $G$, a set $F$ of edges of $G$ is called a \emph{proper cut} if $F$ is an edge-cut of $G$ and any pair of adjacent edges in $F$ are assigned by different colors. An edge-colored graph is \emph{proper disconnected}…