Ordered Coloring Grids and Related Graphs
We investigate a coloring problem, called ordered coloring, in grids and some other families of grid-like graphs. Ordered coloring (also known as vertex ranking) is related to conflict-free coloring and other traditional coloring problems. Such coloring problems can model (among others) efficient frequency assignments in cellular networks. Our main technical results improve upper and lower bounds for the ordered chromatic number of grids and related graphs. To the best of our knowledge, this is the first attempt to calculate exactly the ordered chromatic number of these graph families.
Keywordsgrid graph ordered coloring vertex ranking conflict-free coloring
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- 1.Bar-Noy, A., Cheilaris, P., Smorodinsky, S.: Deterministic conflict-free coloring for intervals: from offline to online. ACM Transactions on Algorithms 4(4), 44:1–44:18 (2008)Google Scholar
- 10.Leiserson, C.E.: Area-efficient graph layouts (for VLSI). In: Proceedings of the 21st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 270–281 (1980)Google Scholar
- 14.Smorodinsky, S.: Combinatorial Problems in Computational Geometry. PhD thesis, School of Computer Science, Tel-Aviv University (2003)Google Scholar