Abstract
In Chaps. 2 and 3, we considered certain vertex colorings induced by edge colorings of a graph; while in Chaps. 4 and 5, we considered certain edge colorings induced by vertex colorings. Proper vertex colorings of graphs and the chromatic number of a graph originated from interest in map colorings. Other vertex colorings were also suggested from map colorings, which induced proper vertex colorings of graphs that often required using fewer colors than the chromatic number of a graph. In this chapter, we describe four such proper colorings originating from map colorings. These four vertex colorings will then be discussed in more detail in Chaps. 7–10.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chartrand, G., Okamoto, F., Zhang, P.: Neighbor-distinguishing vertex colorings of graphs. J. Combin. Math. Combin. Comput. 74, 223–251 (2010)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 The Author
About this chapter
Cite this chapter
Zhang, P. (2016). A Map Coloring Problem. In: A Kaleidoscopic View of Graph Colorings. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-30518-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-30518-9_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30516-5
Online ISBN: 978-3-319-30518-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)