Parallel 5-colouring of planar graphs
We show that a 5-colouring of the vertices of an n-vertex planar graph may be computed in O(log n log* n) time by an exclusive-read exclusive-write parallel RAM with O(n/(log n log* n)) processors. Our algorithm, while faster than all previously known methods, is at the same time the first parallel 5-colouring algorithm to achieve optimal speedup. It should be emphasized that although input to the algorithm is a planar graph, we do not require a planar embedding to be given as part of the input.
Other results concern the colouring of graphs of bounded genus and the construction of search structures for triangular planar subdivisions.
KeywordsPlanar Graph Search Structure Adjacency List Vertex Number Planar Embedding
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