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Given a set S of segments in the plane, the intersection graph of S is the graph with vertex set S in which two vertices are adjacent if and only if the corresponding two segments intersect. We prove… Expand
We consider a network of processors in the absence of unique identities, and study the k-Grouping problem of partitioning the processors into groups of size k and assigning a distinct identity to… Expand
We consider the problem of locating a black hole in synchronous anonymous networks using finite state agents. A black hole is a harmful node in the network that destroys any agent visiting that node… Expand
We prove that every planar graph is an intersection graph of strings in the plane such that any two strings intersect at most once.
We study the problem of locating a particularly dangerous node, the so-called black hole in a synchronous anonymous ring network with mobile agents. A black hole destroys all mobile agents visiting… Expand
A set of identical, mobile agents is deployed in a weighted network. Each agent possesses a battery - a power source allowing the agent to move along network edges. Agents use their batteries… Expand
Simon (Theoret. Comput. Sci. 72 (1990) 65-94) has proved that every morphism from a free semigroup to a finite semigroup S admits a Ramseyan factorization forest of height at most 9|s|. In this… Expand
We prove that every planar graph is the intersection graph of strings in the plane, such that any two strings intersect at most once.
Scott proved in 1997 that for any tree $T$, every graph with bounded clique number which does not contain any subdivision of $T$ as an induced subgraph has bounded chromatic number. Scott also… Expand
We study the problem of mapping an unknown environment represented as an unlabelled undirected graph. A robot (or automaton) starting at a single vertex of the graph G has to traverse the graph and… Expand