Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/36394
題名: 有向圖的視線數
Bar visibility number of oriented graph
作者: 曾煥絢
Tseng, Huan-Hsuan
貢獻者: 張宜武
Chang, Yi-Wu
曾煥絢
Tseng, Huan-Hsuan
關鍵詞: 有向圖
oriented graph
planar
日期: 1997
上傳時間: 18-Sep-2009
摘要: 在張宜武教授的博士論文中研究到視線表示法和視線數。我們以類似的方法定義有向圖的表示法和有向圖的視線數。\r\n首先,我們定義有向圖的視線數為b(D) ,D為有方向性的圖,在論文中可得b(D)≦┌1/2max{△﹢(D),△﹣(D)}┐。另一個重要的結論為考慮一個平面有向圖D,對圖形D上所有的點v,離開點v的邊(進入的邊)是緊鄰在一起時,則可得有向圖的視線數在這圖形上是1(即 b(D)=1)。\r\n另外對特殊的圖形也有其不同的視線數,即對有向完全偶圖Dm,n ,b(Dm,n)≦┌1/2min{m,n}┐ ,而對競賽圖Dn ,可得b(Dn)≦┌n/3┐+1。
In [2], Chang stuidied the bar visibility representations and defined bar visibility number.We defined analogously the bar visibility representation and the bar visibility number of a directed graph D.\r\nFirst we show that the bar visibility number, denoted by b(D),is at most ┌1/2max{△﹢(D),△﹣(D)}┐ if D is an oriented graph.And we show that b(D)=1 for the oriented planar graphs in which all outgoing (incoming) edges of any vertex v of D appear consecutively around v.For any complete bipartite digraph Dm,n ,b(Dm,n)≦┌1/2min{m,n}┐.For any tournament Dn,b(Dn)≦┌n/3┐+1.
參考文獻: REFERENCES
[1] J. A. Boundy and U. S. R. Murty, Graph theory with applications (1976).
[2] Yi-Wu Chang, Bar visibility number, Ph.D. thesis, University of Illinois, 92-102, (1994).
[3] S. Even, Graph Algorithms, Computer Science Press, Rockville, MD, (1979).
[4] A. Lempel, S. Even, and I. Cederbaum, An algorithm for planarity testing of graphs, in Theory of Graphs (Proceedings of an International Symposium, Rome, July 1966), (P. Rosenstiehl, ed.), 215-232, Gordon and Breach, New York, (1967).
[5] Y.-L. Lin and S.S. Skiena, Complexity aspects of visibility graphs, International journal of Computational Geometry & Applications.
<br>[6] L. A. Melnikov, Problem at the Sixth Hungarian Colloquium on Combinatorics, Eger, (1981).
[7] M. Schlag, F. Luccio, P. Maestrini, D. T. Lee, and C. K. Wong, A visibility problem in VLSI layout compaction, in Advances in Compution Research, Vol. 2 (F. P. Preparata, ed.), 259-282, JAI Press Inc.,Greenwich, CT, (1985).
[8] M. Sen, S. Das, A.B. Roy, and D.B. West, Interval digraphs: An analogue of interval graphs, J. Graph Theory, Vol. 13, 189-202 (1989).
[9] R. Tamassia and I. G. Tollis, A unified approach to visibility representations of planar graphs, Discrete and Computational Geometry, Vol. 1, 321-341 (1986).
[10] D. B. West, Degrees and digraphs, Introduction to Graph Theory, 46-49, (1996).
描述: 碩士
國立政治大學
應用數學研究所
85751006
86
資料來源: http://thesis.lib.nccu.edu.tw/record/#B2002001695
資料類型: thesis
Appears in Collections:學位論文

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