2-Tone Colorings in Graph Products

• Autorzy: Jennifer Loe , Danielle Middelbrooks , Ashley Morris , Kirsti Wash
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

t-tone coloring; Cartesian product; direct product; strong product

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 1
• Strony: 55-72

Daty

wydano

2015-02-01

otrzymano

2013-09-13

poprawiono

2014-01-27

zaakceptowano

2014-01-31

online

2015-02-06

Twórcy

autor

Jennifer Loe

• Oklahoma Christian University 2501 E. Memorial Rd. Edmond, OK, 73013, USA,

autor

Danielle Middelbrooks

• Spelman College 350 Spelman Ln. Atlanta, GA 30314, USA,

autor

Ashley Morris

• Savannah State University 3219 College St. Savannah, GA 31404, USA,

autor

Kirsti Wash

• Clemson University Box 340975 Clemson, SC 29634, USA,

Bibliografia

• [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[Crossref][WoS]
• [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. Klavˇzar, 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[Crossref]
• [8] V. Vazirani, Approximation Algorithms (Springer, 2001).

Identyfikatory

DOI

10.7151/dmgt.1773