The game chromatic number and game coloring number of trees and caterpillars

• Main Authors: Tsai Shu-Yu, 蔡叔裕
• Other Authors: Xuding Zhu
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/67904787560440113483

碩士 === 國立中山大學 === 應用數學系 === 87 === In this thesis, we consider the game chromatic number and game coloring number for trees and caterpillars. It is known that the game coloring number of a tree is at most 4 and there exist trees with game coloring number 4. We show the following: (1)10 is the minimum number of vertices for a tree (or caterpillar) with game coloring number 4. (2)14 is the minimum number of vertices for a tree (or caterpillar) with game chromatic number 4. (3)T is a 3-regular caterpillar and |V(T)| not less than 102, then $\chi_g(T) = 4$.