Related papers: An efficient algorithm for the diameter of Cayley …
An L(2,1)-labeling of a graph $G$ is an assignment $f$ from the vertex set $V(G)$ to the set of nonnegative integers such that $|f(x)-f(y)|\ge 2$ if $x$ and $y$ are adjacent and $|f(x)-f(y)|\ge 1$ if $x$ and $y$ are at distance 2, for all…
The search for similarity and dissimilarity measures on phylogenetic trees has been motivated by the computation of consensus trees, the search by similarity in phylogenetic databases, and the assessment of clustering results in…
The results of computer searches for large graphs with given (small) degree and diameter are presented. The new graphs are Cayley graphs of semidirect products of cyclic groups and related groups. One fundamental use of our ``dense graphs''…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…
We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large $k$ and for values of $d$ taken from a large interval, the largest known Cayley…
Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs.…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
We improve upper bounds of F. R. K. Chung and of M. Lu, D. Wan, L.-P. Wang, X.-D. Zhang on the diameter of some Cayley graphs constructed from polynomials over finite fields.
It is known that the number of vertices of a graph of diameter two cannot exceed $d^2+1$. In this contribution we give a new lower bound for orders of Cayley graphs of diameter two in the form $C(d,2)>0.684d^2$ valid for all degrees $d\geq…
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees,…
For a graph $G = (V, E)$, a subset $F\subset V(G)$ is called an $R_k$-vertex-cut of $G$ if $G -F$ is disconnected and each vertex $u \in V(G)- F$ has at least $k$ neighbors in $G -F$. The $R_k$-vertex-connectivity of $G$, denoted by…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
We consider drawings of graphs in the plane in which vertices are assigned distinct points in the plane and edges are drawn as simple curves connecting the vertices and such that the edges intersect only at their common endpoints. There is…
It is known that any planar graph with diameter D has treewidth O(D), and this fact has been used as the basis for several planar graph algorithms. We investigate the extent to which similar relations hold in other graph families. We show…
In 1996, Bodlaender showed the celebrated result that an optimal tree decomposition of a graph of bounded treewidth can be found in linear time. The algorithm is based on an algorithm of Bodlaender and Kloks that computes an optimal tree…
Given a group G, the model $\mathcal{G}(G,p)$ denotes the probability space of all Cayley graphs of G where each element of the generating set is chosen independently at random with probability p. In this article we show that for any…
Given a group $G$, the model $\mathcal{G}(G,p)$ denotes the probability space of all Cayley graphs of $G$ where each element of $G$ is included in the generating set independently at random with probability $p$. In this article, we…
We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can attain. We first…
In this paper, we present an exact algorithm for the Steiner tree problem. The algorithm is based on certain pre-computed index structures. Our algorithm offers a practical solution for the Steiner tree problems on graphs of large size and…
We show how to construct an overlay network of constant degree and diameter $O(\log n)$ in time $O(\log n)$ starting from an arbitrary weakly connected graph. We assume a synchronous communication network in which nodes can send messages to…