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.

Source : oai:HAL:hal-01188906v1

Volume: Vol. 16 no. 3 (in progress)

Section: Graph Theory

Published on: June 19, 2014

Submitted on: November 14, 2012

Keywords: graph colouring,homomorphism,vertex partitions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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