# Coloring subgraphs with restricted amounts of hues

Wayne Goddard; Robert Melville

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1171-1180
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topWayne 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.