Coloring the Cartesian sum of graphs

For graphs G and H, let G H denote their Cartesian sum. This paper investigates the chromatic number and the circular chromatic number for GH. It is proved that (G H) max{ c(G)(H) , (G)c(H) } holds for any G and H; and c(G H) max{(H)c(G), (G)c(H)} holds for graphs G and H with some special values of c(G) and c(H). These results improve previously known bounds on the corresponding coloring parameters for the Cartesian sum of graphs. 1991 Mathematics Subject Classification. 05C20, 05C35, 05C15 Key words and phrases: Cartesian sum of graphs, chromatic number, circular chromatic number, fractional chromatic number. Supported by the National Science Foundation, USA, under grant DMS 0302456. Supported by the National Science Council, Taiwan, under grant NSC93-2115-M-110-004. 1 

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Daphne Der-Fen Liu, Xuding Zhu
• Keywords: Cartesian Sum, Chromatic Number, Circular Chromatic Number, DM 2008