Geodesic
2-Tone Colorings in Graph Products
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 55-72.

Voir la notice de l'article provenant de la source Library of Science

A variation of graph coloring known as a t-tone k-coloring assigns a set of t colors to each vertex of a graph from the set 1, . . ., k, where the sets of colors assigned to any two vertices distance d apart share fewer than d colors in common. The minimum integer k such that a graph G has a t- tone k-coloring is known as the t-tone chromatic number. We study the 2-tone chromatic number in three different graph products. In particular, given graphs G and H, we bound the 2-tone chromatic number for the direct product G×H, the Cartesian product G□H, and the strong product G⊠H.
Keywords: t-tone coloring, Cartesian product, direct product, strong product 
@article{DMGT_2015_35_1_a4,
     author = {Loe, Jennifer and Middelbrooks, Danielle and Morris, Ashley and Wash, Kirsti},
     title = {2-Tone {Colorings} in {Graph} {Products}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {55--72},
     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a4/}
}
TY  - JOUR
AU  - Loe, Jennifer
AU  - Middelbrooks, Danielle
AU  - Morris, Ashley
AU  - Wash, Kirsti
TI  - 2-Tone Colorings in Graph Products
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2015
SP  - 55
EP  - 72
VL  - 35
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a4/
LA  - en
ID  - DMGT_2015_35_1_a4
ER  - 
%0 Journal Article
%A Loe, Jennifer
%A Middelbrooks, Danielle
%A Morris, Ashley
%A Wash, Kirsti
%T 2-Tone Colorings in Graph Products
%J Discussiones Mathematicae. Graph Theory
%D 2015
%P 55-72
%V 35
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a4/
%G en
%F DMGT_2015_35_1_a4
Loe, Jennifer; Middelbrooks, Danielle; Morris, Ashley; Wash, Kirsti. 2-Tone Colorings in Graph Products. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 55-72. http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a4/

[1] A. Bickle and B. Phillips, t-tone colorings of graphs, submitted (2011).

[2] D. Cranston, J. Kim and W. Kinnersley, New results in t-tone colorings of graphs, Electron. J. Comb. 20(2) (2013) #17.

[3] D. Bal, P. Bennett, A. Dudek and A. Frieze, The t-tone chromatic number of random graphs, Graphs Combin. 30 (2013) 1073-1086. doi:10.1007/s00373-013-1341-9

[4] N. Fonger, J. Goss, B. Phillips and C. Segroves, Math 6450: Final Report, (2011). http://homepages.wmich.edu/~zhang/finalReport2.pdf

[5] D. West, REGS in Combinatorics. t-tone colorings, (2011). http://www.math.uiuc.edu/~west/regs/ttone.html

[6] R. Hammack, W. Imrich and S. Klavžar, Handbook of Product Graphs, Second Edition (CRC Press, Boca Raton, 2011).

[7] S. Krumke, M. Marathe and S. Ravi, Approximation algorithms for channel assignment in radio networks, Wireless Networks 7 (2001) 575-584. doi:10.1023/A:1012311216333

[8] V. Vazirani, Approximation Algorithms (Springer, 2001).