Broadcasting in DMA-bound 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...

Independent Sets near the Lower Bound in Bounded Degree Graphs

By Brook’s Theorem, every n-vertex graph of maximum degree at most ∆ ≥ 3 and clique number at most ∆ is ∆-colorable, and thus it has an independent set of size at least n/∆. We give an approximate characterization of graphs with independence number close to this bound, and use it to show that the problem of deciding whether such a graph has an indepdendent set of size at least n/∆ + k has a ker...

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