Coloring subgraphs with restricted amounts of hues

Wayne Goddard, and Robert Melville. "Coloring subgraphs with restricted amounts of hues." Open Mathematics 15.1 (2017): 1171-1180. <http://eudml.org/doc/288331>.

@article{WayneGoddard2017,
abstract = {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.},
author = {Wayne Goddard, Robert Melville},
journal = {Open Mathematics},
keywords = {Vertex colorings; Rainbow; Monochromatic; Defective},
language = {eng},
number = {1},
pages = {1171-1180},
title = {Coloring subgraphs with restricted amounts of hues},
url = {http://eudml.org/doc/288331},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Wayne Goddard
AU - Robert Melville
TI - Coloring subgraphs with restricted amounts of hues
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1171
EP - 1180
AB - 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.
LA - eng
KW - Vertex colorings; Rainbow; Monochromatic; Defective
UR - http://eudml.org/doc/288331
ER -