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Complexity of conditional colouring with given template

Abstract : We study partitions of the vertex set of a given graph into cells that each induce a subgraph in a given family, and for which edges can have ends in different cells only when those cells correspond to adjacent vertices of a fixed template graph H. For triangle-free templates, a general collection of graph families for which the partitioning problem can be solved in polynomial time is described. For templates with a triangle, the problem is in some cases shown to be NP-complete.
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Submitted on : Monday, August 31, 2015 - 5:03:28 PM
Last modification on : Friday, June 1, 2018 - 3:24:01 PM
Long-term archiving on: : Tuesday, December 1, 2015 - 10:43:02 AM


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  • HAL Id : hal-01188906, version 1



Peter J. Dukes, Steve Lowdon, Gary Macgillivray. Complexity of conditional colouring with given template. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (in progress) (3), pp.61--76. ⟨hal-01188906⟩



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