Broadcasting in Bounded Degree Graphs

Broadcasting in Bounded Degree Graphs

Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. Several previous papers have investigated methods to construct sparse graphs (networks) in which this process can be completed in minimum time from any originator. The graphs produced by these met...

Broadcasting on Bounded Degree DAGs

We study the following generalization of the well-known model of broadcasting on trees. Consider an infinite directed acyclic graph (DAG) with a unique source node X . Let the collection of nodes at distance k from X be called the kth layer. At time zero, the source node is given a bit. At time k ≥ 1, each node in the (k − 1)th layer inspects its inputs and sends a bit to its descendants in the...

k-forested choosability of graphs with bounded maximum average degree

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...

Spanners of bounded degree graphs

Sparse universal graphs for bounded-degree graphs

Let H be a family of graphs. A graph T is H-universal if it contains a copy of each H ∈ H as a subgraph. Let H(k, n) denote the family of graphs on n vertices with maximum degree at most k. For all positive integers k and n, we construct an H(k, n)-universal graph T with Ok(n 2 k log 4 k n) edges and exactly n vertices. The number of edges is almost as small as possible, as Ω(n2−2/k) is a lower...