A conflict-free k-coloring of a graph G = (V,E) assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v’s neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory. Here we study the conflictfree coloring of geometric inter...

A disk graph is the intersection graph of disks in the plane, a unit disk graph is the intersection graph of same radius disks in the plane, and a segment graph is an intersection graph of line segments in the plane. Every disk graph can be realized by disks with centers on the integer grid and with integer radii; and similarly every unit disk graph can be realized by disks with centers on the ...

In this paper, the space requirements for the OBDD representation of certain graph classes, specifically cographs, several types of graphs with few P4s, unit interval graphs, interval graphs and bipartite graphs are investigated. Upper and lower bounds are proven for all these graph classes and it is shown that in most (but not all) cases a representation of the graphs by OBDDs is advantageous ...

In this paper, we design the first polynomial time approximation scheme for d-hop connected dominating set (d-CDS) problem in growth-bounded graphs, which is a general type of graphs including unit disk graph, unit ball graph, etc. Such graphs can represent majority types of existing wireless networks. Our algorithm does not need geometric representation (e.g., specifying the positions of each ...

When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations. A simple idea to account for multiple constraints consists in taking the intersection of random graphs. In this paper we initiate the study of random graphs ...

We study the online graph coloring problem restricted to the intersection graphs of intervals with lengths in [1, σ]. For σ = 1 it is the class of unit interval graphs, and for σ =∞ the class of all interval graphs. Our focus is on intermediary classes. We present a (1 + σ)-competitive algorithm, which beats the state of the art for 1 < σ < 2. For σ = 1 our algorithm matches the performance of ...

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

We present 1 − approximation algorithms for the maximum matching problem in location aware unit disc graphs and in growth-bounded graphs. The algorithm for unit disk graph is local in the sense that whether or not an edge is in the matching depends only on other vertices which are at most a constant number of hops away from it. The algorithm for growth-bounded graphs needs at most O ( log4 log∗...