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For a positive integer k, a k-packing in a graph G is a subset A of vertices such that the distance between any two distinct vertices from A is more than k. The packing chromatic number of G is the smallest integer m such that the vertex set of G can be partitioned as V1, V2,. .. , Vm where Vi is an i-packing for each i. It is proved that the planar(More)
Fires (or viruses) break out at a set S of f vertices in a connected simple graph G. Each of d defenders protects one node that is not yet on fire (infected). The fires (viruses) then spread to any neighbouring unprotected nodes. The fires and defenders (firefighters) take turns until the fires can no longer spread. Assume that the firefighters, confronted(More)
A graph G is said to be well-covered if every maximal independent set of vertices has the same cardinality. A planar (simple) graph in which each face is a triangle is called a triangulation. It was proved in an earlier paper [A. 97–108] that there are no 5-connected planar well-covered triangulations. It is the aim of the present paper to completely(More)