We consider vertex colorings where the number of colors given to specified subgraphs is restricted. In particular, given some fixed graph F and some fixed set A of positive integers, we consider (not necessarily proper) colorings of the vertices of a graph G such that, for every copy of F in G, the number of colors it receives is in A. This generalizes proper colorings, defective coloring, and no-rainbow coloring, inter alia. In this paper we focus on the case that A is a singleton set. In particular, we investigate the colorings where the graph F is a star or is 1-regular.
@article{bwmeta1.element.doi-10_1515_math-2017-0098,
author = {Wayne Goddard and Robert Melville},
title = {Coloring subgraphs with restricted amounts of hues},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1171-1180},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0098}
}
Wayne Goddard; Robert Melville. Coloring subgraphs with restricted amounts of hues. Open Mathematics, Tome 15 (2017) pp. 1171-1180. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0098/