摘要
In this paper, we focus on the oriented coloring of a graph G. Oriented coloring is a coloring of the vertices of an oriented graph H such that (1) no two neighbors in H are assigned in the same color, and (2) for every two arcs u→v and x→y, if v and x are assigned the same color then u and y cannot be assigned the same color. The oriented chromatic number of a graph G is the maximum oriented chromatic number over all possible orientations of G. In this paper, we derive a lower bound and an upper bound on the oriented chromatic number of honeycomb rectangular tori. Finally, we conjecture to the oriented chromatic number of honeycomb rectangular tori is 10.
延伸閱讀
- Kuo, C. C. (2009). Randomly Coloring Regular Bipartite Graphs and Graphs with Bounded Common Neighbors [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2009.00953
- 吳淵渟（2000）。A Fault-Containing Self-Stabilizing Algorithm for coloring planar graphs〔碩士論文，元智大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0009-0112200611300870
- Weng, Y. C. (2008). On the IC-Colorings of Split Graphs [master's thesis, Chung Yuan Christian University]. Airiti Library. https://doi.org/10.6840/CYCU.2008.00414
- Tsai, C. H. (2012). On the IC-colorings of complete tripartite graphs K(1,m,n) [master's thesis, Chung Yuan Christian University]. Airiti Library. https://doi.org/10.6840/cycu201200233
- Hung, P. H. (2005). On the Equitable Coloring of Halin Graphs [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2005.01813