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論文名稱 Title |
哈林圖的對局色數 Game chromatic number of Halin graphs |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
30 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2001-06-01 |
繳交日期 Date of Submission |
2001-06-27 |
關鍵字 Keywords |
對局色數、哈林圖 Game chromatic number, Halin graphs |
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統計 Statistics |
本論文已被瀏覽 5730 次,被下載 1953 次 The thesis/dissertation has been browsed 5730 times, has been downloaded 1953 times. |
中文摘要 |
論文摘要內容: 本論文在於探討哈林圖的對局色數. 我們將證明除了兩個哈林圖以外的其他哈林圖的對局色數都等於4. 這個遊戲是有兩個人在玩, 分別是愛麗絲和鮑伯, 給一個圖和顏色集, 由愛麗絲和鮑伯從顏色集裡找一個顏色在圖上的頂點著色, 使得相鄰兩點不可著同一個顏色. 順序由愛麗絲先動, 再換鮑伯, 輪流在圖上著色. 一直玩到最後, 如果每一個點都被著色了, 則為愛麗絲臝. 反之, 則為鮑伯贏. 對局色數為給最少的顏色使得愛麗絲又能獲勝的顏色數. 哈林圖為一種特別的平面圖, 包含了一個樹和一個圈, 其中圈上的點都是頂點都是樹上的葉, 並且除了葉以外, 其餘樹上的頂點的度都大於或等於3. |
Abstract |
This thesis discusses the game chromatic number of Halin graphs. We shall prove that with a few exceptions, all Halin graphs have game chromatic number 4. |
目次 Table of Contents |
1 Introduction 1 1.1 Definition of ˜g and colg . . . . . . . . . . . . . . . . . . . . . 1 1.2 Halin graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Main result . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Proof of the main result 6 2.1 Game coloring number and proof of the upper bound . . . . . 6 2.2 Some preliminary lemmas . . . . . . . . . . . . . . . . . . . . 8 2.3 First colored vertex lies on C . . . . . . . . . . . . . . . . . . 12 2.4 First colored vertex does not lie on C . . . . . . . . . . . . . . 19 |
參考文獻 References |
[1] Barefoot, C. A, 4-connected Halin graphs are 2-Hamiltonian connected, Ars Combin. 35 (1993), A, 109–128. [2] Lam, Peter C. B.; Zhang, Zhongfu The vertex-face total chromatic num-ber of Halin graphs, Networks 30 (1997), no. 3, 167–170. [3] H.L. Bodlaender, On the complexity of some coloring games, Computer Science, 30-40, Springer-Verlag, 1991. [4] Leizhen Cai and X.Zhu, The game chromatic index and game coloring index of graphs, J. Graph Theory, to appear. [5] T.Dinski and X.Zhu, An upper bound for the game chromatic of graphs, Discrete Mathematic, 11 (1998),590-602. [6] U.Faigle, U. kern ,H. Kierstead and W. T. Trotter, On the game chro-matic number of some classes of graphs, Ars Combin. 35 (1993),143-150. [7] Zhang, Zhong Fu; Lu, Xin Zhong; Liu, Ming Hua Edge-face total chro-matic numbers of Halin graphs Hg with maximum degree (Hg) 7 and (Hg) = 4, 5, 6, (Chinese) J. Lanzhou Railway Inst. 12 (1993), no. 4, 90–95. [8] D. Guan and X.Zhu, The game chromatic number of outerplanar graphs, Journal of Graph Theory, 30(1999),67-70. [9] T. Jensen and B. Toft, Graph coloring Problems, John Wiley [10] Lou, Ding Jun, Hamiltonian paths in Halin graphs, Math. Appl. 8 (1995), no. 2, 158–160. [11] H.A. Kierstead and W.T. Trotter, Planar graph coloring With an unco-operative partner, J. Graph Theory 18 (1994), no. 6, 569-584. [12] H. A. Kierstead, A simple competitive graph coloring algorithm, Journal of Combinatorial Theory (B), 78(2000), 57-68. 1998. [13] Ko-Wei Lih and Weifan Wang, Some results on game coloring a graph, 2000. [14] Phillips, Jeffrey Mark; Punnen, Abraham P.; Kabadi, S. N, Alinear time algorithm for the bottleneck traveling salesman problem on a Halin graph, Inform. Process. Lett. 67 (1998), no. 2, 105–110. [15] C.St. J. A. Nash-William, Decomposition of finite graphs into forest, J. London Math. Soc. 39(1964). [16] Easton, Todd; Horton, Steve; Parker, R. Gary, A solvable case of the optimal linear arrangement problem on Halin graphs, Congr. Numer. 119 (1996), 3–17. [17] Zhang, Zhongfu; Liu, Linzhong; Wang, Jianfang; Li, Hongxiang, A note on the total chromatic number of Halin graphs with maximum degree 4, Appl. Math. Lett. 11 (1998), no. 5, 23–27. [18] X. Zhu, The game coloring number of pseudo partial k-trees, Discrete Mathematic, to appear. [19] X. Zhu, Game coloring number of planar graphs, Journal of Combina-torial Theory (B), 75(1999),245-258. [20] X. Zhu, On the game coloring number of graphs, manuscript, 1998. |
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